Faculty Profiles - SAKAMOTO SHOTA

Information

写真a

SAKAMOTO SHOTA

Organization

Faculty of Mathematics Division of Analysis Associate Professor
School of Sciences Department of Mathematics（Concurrent）
Graduate School of Mathematics Department of Mathematics（Concurrent）
Joint Graduate School of Mathematics for Innovation （Concurrent）

Profile

偏微分方程式、特にボルツマン方程式を中心とする分子気体運動論に現れる方程式の解の存在や一意性、正則性などの性質を関数解析的手法を用いて研究しています。

Homepage

https://sites.google.com/view/shota-sakamoto/home

External link

Research History

Kyushu University Faculty of Mathematics Associate Professor

2023.4 - Present

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Country：Japan

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Tokyo Institute of Technology Department of Mathematics, School of Science Assistant Professor

2020.4 - 2023.3

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Country：Japan

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Research Interests・Research Keywords

Research theme： Kinetic equations

Keyword： Kinetic equations

Research period： 2024
Research theme： Partial differential equations

Keyword： Partial differential equations

Research period： 2024
Research theme： Landau equation

Keyword： Landau equation

Research period： 2024
Research theme： Boltzmann equation

Keyword： Boltzmann equation

Research period： 2024
Research theme： My research interests are study of various kinetic equations, particularly the non cut-off Boltzmann equation. I study the existence, uniqueness, and regularity of solutions to a Cauchy problem of the equation. My main results are: the construction of a global solution to the non cut-off Boltzmann equation near the global equilibrium in Besov spaces over the whole space[Morimoto and S., J. Differential Equation 261(2016)], and the construction of a global solution to the equation near the equilibrium in the Wiener space over the torus and the strip [Duan et al., Comm. Pure Appl. Math. 74(2021)]. The uniqueness of solutions and their time-decay rates are also proved. I will study the regularity of the obtained solutions, and the construction of solutions to the equation with more slowly decaying initial data.

Keyword： Partial differential equations, kinetic equations, Boltzmann equation, existence and uniqueness of a solution

Research period： 2016.4

Papers

An $\boldsymbol{L^1_{k}\cap L^{p}_{k } }$ Approach for the Non-Cutoff Boltzmann Equation in $\boldsymbol{\mathbb{R}^3}$ Reviewed

Renjun Duan, Shota Sakamoto, Yoshihiro Ueda

SIAM Journal on Mathematical Analysis 56 ( 1 ) 762 - 800 2024 （ ISSN:0036-1410 eISSN:1095-7154 ）

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Language：English Publishing type：Research paper (scientific journal) Publisher：Society for Industrial & Applied Mathematics (SIAM)

In the paper, we develop an L1k ∩ Lpk approach to construct global solutions to the Cauchy problem on the non-cutoff Boltzmann equation near equilibrium in ℝ3. In particular, only smallness of ||Fxf0||L1∩Lp(ℝ3k;L2(ℝ3v)) with 3/2 < p ≤ ∞ is imposed on initial data f0(x, v), where Fxf0(k, v) is the Fourier transform in space variable. This provides the first result on the global existence of such low-regularity solutions without relying on Sobolev embedding H2(ℝ3x) ⊂ L∞(ℝ3x) in the case of the whole space. Different from the use of sufficiently smooth Sobolev spaces in the classical results [P. T. Gressman and R. M. Strain, J. Amer. Math. Soc., 24 (2011), pp. 771-847] and [R. Alexandre et al., J. Funct. Anal., 262 (2012), pp. 915-1010], there is a crucial difference between the torus case and the whole space case for low-regularity solutions under consideration. In fact, for the former, it is enough to take the only L1k norm corresponding to the Weiner space as studied in [R. J. Duan et al., Comm. Pure Appl. Math., 74 (2021), pp. 932-1020]. In contrast, for the latter, the extra interplay with the Lpk norm plays a vital role in controlling the nonlinear collision term due to the degenerate dissipation of the macroscopic component. Indeed, the propagation of the Lpk norm helps gain an almost optimal decay rate (1+t)-32 (1- p1)+ of the L1k norm via the time-weighted energy estimates in the spirit of the idea of [S. Kawashima, J. Hyperbolic Differ. Equ., 1 (2004), pp. 581-603] and, in turn, this is necessarily used for establishing the global existence.

DOI： 10.1137/22M1533232

Web of Science

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Global Mild Solutions of the Landau and Non‐Cutoff Boltzmann Equations Reviewed

Renjun Duan, Shuangqian Liu, Shota Sakamoto, Robert M. Strain

Communications on Pure and Applied Mathematics 2020.6

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本論文ではランダウ方程式及び非切断ボルツマン方程式の定常解周りの初期値及び初期値境界値問題の解について考察した。これ以前の研究では、L^2空間を基にするSobolev空間やBesov空間などを用いた研究が主であり、その場合空間がHilbertであることが証明の中で本質的に使われていた。本論文ではFourier級数の絶対総和可能性で特徴づけられる、Wiener空間と呼ばれるクラスを用いて、領域が3次元トーラスの場合の初期値問題、領域が3次元の帯状領域(2次元トーラスと1次元区間の積)の場合に物理的に自然ないくつかの境界条件を課した初期値境界値問題に対して、解のの一意存在とその時間減衰レートを証明した。

DOI： 10.1002/cpa.21920

Repository Public URL： https://hdl.handle.net/2324/7174347
Global solutions in the critical Besov space for the non-cutoff Boltzmann equation Reviewed

Yoshinori Morimoto, Shota Sakamoto

JOURNAL OF DIFFERENTIAL EQUATIONS 261 ( 7 ) 4073 - 4134 2016.10

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Language：English Publishing type：Research paper (scientific journal)

The Boltzmann equation is studied without the cutoff assumption. Under a perturbative setting, a unique global solution of the Cauchy problem of the equation is established in a critical Chemin-Lerner space. In order to analyze the collisional term of the equation, a Chemin-Lerner norm is combined with a non isotropic norm with respect to a velocity variable, which yields an a priori estimate for an energy estimate. Together with local existence following from commutator estimates and the Hahn-Banach extension theorem, the desired solution is obtained. (C) 2016 Elsevier Inc. All rights reserved.

DOI： 10.1016/j.jde.2016.06.017
Solution to the Boltzmann equation whose Fourier transform are integrable (Mathematical Analysis in Fluid and Gas Dynamics)

Sakamoto Shota

RIMS Kokyuroku 2282 104 - 115 2024.5 （ ISSN:18802818 ）

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Language：English Publisher：京都大学数理解析研究所

CiNii Research
Global solutions to an equation for mutation process in bacteria and its preservation of positive supports Reviewed

Shota Sakamoto

Journal of Mathematical Analysis and Applications 507 ( 1 ) 125771 - 125771 2022.3 （ ISSN:0022-247X ）

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Language：English Publishing type：Research paper (scientific journal) Publisher：Elsevier BV

An equation describing mutation process in bacteria is considered in the form of a kinetic equation. The existence of a unique global solution to the Fourier-transformed equation is shown in spaces of characteristic functions whose corresponding probability measures possess finite moments. Due to correspondences of such spaces of probability measures and those of characteristic functions, a unique global probability measure solution to the original equation is found in the weak sense. Moreover, it is shown that if the support of the initial data is in R+, then that of the solution is also in R+. The proof is based on a contraction argument applied to the spatially homogeneous Boltzmann equation and the analysis of a solution as a boundary characteristic function.

DOI： 10.1016/j.jmaa.2021.125771

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Boundary layers of the Boltzmann equation in three-dimensional half-space Reviewed

Shota Sakamoto, Masahiro Suzuki, Katherine Zhiyuan Zhang

Journal of Differential Equations 314 446 - 472 2022.3 （ ISSN:0022-0396 ）

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Language：English Publishing type：Research paper (scientific journal) Publisher：Elsevier BV

We consider the nonlinear boundary layers of the Boltzmann equation on a three-dimensional half-space by perturbing around a Maxwellian under the assumption that the Mach number of the Maxwellian satisfies M∞<−1. In earlier works by S. Ukai, T. Yang, S.-H. Yu, nonlinear boundary layers of the Boltzmann equation in a half-line are considered, in a half-line are considered, the stationary solutions were obtained and nonlinear stability was confirmed. We establish the existence and uniqueness of stationary and time-periodic solutions for the three-dimensional half-space model and show that these solutions are asymptotically stable.

DOI： 10.1016/j.jde.2022.01.023

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Spectra of expanding maps on Besov spaces Reviewed

Yushi Nakano, Shota Sakamoto

Discrete and Continuous Dynamical Systems 39 ( 4 ) 1779 - 1797 2019.4

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Language：English Publishing type：Research paper (scientific journal)

Spectra of expanding maps on Besov spaces
© 2019 American Institute of Mathematical Sciences. All Rights Reserved. A typical approach to analysing statistical properties of expanding maps is to show spectral gaps of associated transfer operators in adapted function spaces. The classical function spaces for this purpose are Hölder spaces and Sobolev spaces. Natural generalisations of these spaces are Besov spaces, on which we show a spectral gap of transfer operators.

DOI： 10.3934/dcds.2019077
Solution to the Boltzmann equation in velocity-weighted Chemin-Lerner type spaces Reviewed

Renjun Duan, Shota Sakamoto

Kinetic and Related Models 11 ( 6 ) 1301 - 1331 2018.12

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In this paper the Boltzmann equation near global Maxwellians is studied in the d-dimensional whole space. A unique global-in-time mild solution to the Cauchy problem of the equation is established in a Chemin-Lerner type space with respect to the phase variable (x
v). Both hard and soft potentials with angular cutoff are considered. The new function space for global well-posedness is introduced to essentially treat the case of soft potentials, and the key point is that the velocity variable is taken in the weighted supremum norm, and the space variable is in the s-order Besov space with s ≥ d/2 including the spatially critical regularity. The proof is based on the time-decay properties of solutions to the linearized equation together with the bootstrap argument. Particularly, the linear analysis in case of hard potentials is due to the semigroup theory, where the extra time-decay plays a role in coping with initial data in L2 with respect to the space variable. In case of soft potentials, for the time-decay of linear equations we borrow the results based on the pure energy method and further extend them to those in L∞ framework through the technique of L2-L∞ interplay. In contrast to hard potentials, L1 integrability in x of initial data is necessary for soft potentials in order to obtain global solutions to the nonlinear Cauchy problem.

DOI： 10.3934/krm.2018051
SOME REMARKS ON THE HOMOGENEOUS BOLTZMANN EQUATION WITH THE FRACTIONAL LAPLACIAN TERM Reviewed

Shota Sakamoto

OSAKA JOURNAL OF MATHEMATICS 53 ( 3 ) 621 - 636 2016.7

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We study the homogeneous Boltzmann equation with the fractional Laplacian term. Working on the Fourier side we solve the resulting integral equation, and improve a previous result by Y.-K. Cho. We replace the initial data space with a certain space M-alpha introduced by Morimoto, Wang, and Yang. This space precisely captures the Fourier image of probability measures with bounded fractional moments, providing a more natural initial condition. We show existence of a unique global solution, in addition to the expected maximal growth estimates and stability estimates. As a consequence we obtain a continuous density solution of the original equation.

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Presentations

Fourier変換の可積分性で特徴づけられる非切断ボルツマン方程式の大域解 Invited

坂本祥太

微分方程式の総合的研究 2023.12

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Event date： 2023.12

Language：Japanese

Country：Japan

Global solutions to the Boltzmann equation without angular cut-off that are characterized by integrability of their Fourier transform
Global solutions to the Boltzmann equation without angular cut-off that are characterized by integrability of their Fourier transform Invited

坂本祥太

微分方程式の総合的研究 2023.12

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Event date： 2023.12

Language：Japanese Presentation type：Oral presentation (invited, special)

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Global solutions to the non cutoff Boltzmann equation with low-regularity initial data Invited International conference

偏微分方程式姫路研究集会 (2025) 2025.3

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Event date： 2025.3

Language：English Presentation type：Oral presentation (invited, special)

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Faster decay of the microscopic part of a solution to the Boltzmann equation Invited International conference

Shota Sakamoto

Workshop on PDE Week-Kinetic and Related Topics 2024.2

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Event date： 2024.2

Language：English
Faster decay of the microscopic part of a solution to the Boltzmann equation Invited

Shota Sakamoto

Workshop on PDE Week-Kinetic and Related Topics 2024.2

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Event date： 2024.2

Language：English Presentation type：Oral presentation (invited, special)

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Faster decay of the microscopic part of a solution to the Boltzmann equation Invited International conference

Shota Sakamoto

CM2LA Seorabeol Research Station: Workshop in Kinetic Theory 2024.1

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Event date： 2024.1

Language：English

Venue：POSTECH Country：Korea, Republic of
Faster decay of the microscopic part of a solution to the Boltzmann equation Invited

Shota Sakamoto

CM2LA Seorabeol Research Station: Workshop in Kinetic Theory 2024.1

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Event date： 2024.1

Language：English Presentation type：Oral presentation (invited, special)

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Faster decay of the microscopic part of a solution to the Boltzmann equation without angular cut-off Invited International conference

Shota Sakamoto

East Asian Workshop on PDEs from Kinetics and Continuum Mechanics 2023.11

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Event date： 2023.11

Language：English

Country：Japan
Faster decay of the microscopic part of a solution to the Boltzmann equation without angular cut-off Invited International conference

Shota Sakamoto

East Asian Workshop on PDEs from Kinetics and Continuum Mechanics 2023.11

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Event date： 2023.11

Language：English Presentation type：Oral presentation (invited, special)

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Solution to the Boltzmann equation without cutoff in $(L^1cap L^p)_k$ Invited International conference

Shota Sakamoto

ICIAM 2023 2023.8

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Event date： 2023.8

Language：English

Venue：Tokyo Country：Japan
Solution to the Boltzmann equation without cutoff in $(L^1\cap L^p)_k$ Invited

Shota Sakamoto

ICIAM 2023 2023.8

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Event date： 2023.8

Language：English Presentation type：Oral presentation (general)

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Global solution to the Boltzmann equation without angular cutoff in $(L^1 \cap L^p)_k$ Invited International coauthorship International conference

Shota Sakamoto

Mathematical Analysis in Fluid and Gas Dynamics 2023.7

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Event date： 2023.7

Language：English Presentation type：Oral presentation (invited, special)

Venue：Kyoto University Country：Japan

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Global solution to the Boltzmann equation without cutoff on the whole space in $(L^1 cap L^p)_k$ Invited

Shota Sakamoto

Kyoto-CAU Joint Meeting on Nonlinear PDEs 2023.3

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Event date： 2023.3

Language：English

Country：Japan
Global solution to the Boltzmann equation without cutoff on the whole space in $(L^1 \cap L^p)_k$ Invited

Shota Sakamoto

Kyoto-CAU Joint Meeting on Nonlinear PDEs 2023.3

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Event date： 2023.3

Language：English Presentation type：Oral presentation (invited, special)

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A Cauchy problem of the Boltzmann equation without angular cutoff near an equilibrium in low-regularity spaces Invited

Shota Sakamoto

Rigorous Statistical Mechanics and Related Topics 2022.11

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Event date： 2022.11

Language：English

Venue：Kyoto Country：Japan
A Cauchy problem of the Boltzmann equation without angular cutoff near an equilibrium in low-regularity spaces Invited

Shota Sakamoto

Rigorous Statistical Mechanics and Related Topics 2022.11 RIMS, Kyoto University

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Event date： 2022.11

Language：English Presentation type：Oral presentation (invited, special)

Venue：Kyoto Country：Japan

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Global solution to the Boltzmann equation without angular cutoff in a low-regularity space on the whole space Invited International conference

Shota Sakamoto

The Eighth Japan-China Workshop on Mathematical Topics from Fluid Mechanics 2022.10

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Event date： 2022.10

Language：English

Venue：オンライン Country：Japan
Global solution to the Boltzmann equation without angular cutoff in a low-regularity space on the whole space Invited

Shota Sakamoto

The Eighth Japan-China Workshop on Mathematical Topics from Fluid Mechanics 2022.10

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Event date： 2022.10

Language：English Presentation type：Oral presentation (invited, special)

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The well-posedness of the Boltzmann equation without angular cutoff in some Banach-algebra spaces Invited International conference

Shota Sakamoto

International Workshop on Multi-Phase Flows: Analysis, Modelling and Numerics 2021.11

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Event date： 2021.11 - 2021.12

Language：English

Venue：オンライン Country：Japan
The stability of a solution to the Boltzmann equation in the 3D half-space Invited International conference

Shota Sakamoto

International Workshop on Recent Advances in Nonlinear PDEs 2021.6

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Event date： 2021.6

Language：English

Venue：Nanjing (online) Country：China
The stability of a solution to the Boltzmann equation in the 3D half-space Invited International coauthorship International conference

Shota Sakamoto

International Workshop on Recent Advances in Nonlinear PDEs 2021.6

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Event date： 2021.6

Language：English Presentation type：Oral presentation (invited, special)

Venue：Nanjing (online) Country：China

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3次元半空間におけるボルツマン方程式の初期値境界値問題の漸近安定性

坂本祥太, 鈴木政尋, Katherine Zhiyuan Zhang

日本数学会2021年度年会 2021.3

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Event date： 2021.3

Language：Others

Country：Other
圧縮性粘性流の初期値問題 Invited

坂本祥太

第４回白浜研究集会 2012.12

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Language：Japanese

Venue：紀州・白浜温泉旅館むさし Country：Other

Initial value problem of viscous compressible flows
Wasserstein計量を用いた運動論的Fokker-Planck方程式の解の構成 Invited

坂本祥太

第5回白浜研究集会 2013.12

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Language：Japanese

Venue：南紀白浜温泉白浜御苑 Country：Other

Construction of a solution to a kinetic Fokker-Planck equation via the Wasserstein metric
Wasserstein計量を用いた運動論的Fokker-Planck方程式の解の構成 Invited

坂本祥太

確率論早春セミナー 2014.3

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Language：Japanese

Venue：京都大学 Country：Other

Construction of a solution to a kinetic Fokker-Planck equation via the Wasserstein metric
空間一様・マクスウェル型で拡散項を持つボルツマン方程式の解について

坂本祥太

2014年度偏微分方程式論集中セミナー 2014.8

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Language：Japanese

Venue：城崎国際アートセンター Country：Other

Solution to the spatially homogeneous Boltzmann equation for Maxwellian molecules with a fractional term
Some remarks on the homogeneous Boltzmann equation with the fractional Laplacian term Invited International conference

坂本祥太

Doctorial Forum of Mathematics between Fudan and Kyoto Universities 2014.11

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Language：English

Venue：復旦大学 Country：China

Some remarks on the homogeneous Boltzmann equation with the fractional Laplacian term
拡散項付きボルツマン方程式の無限エネルギー解 Invited

坂本祥太

第６回白浜研究集会 2014.12

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Language：Japanese

Venue：紀州・白浜温泉旅館むさし Country：Other

Infinite energy solutions to the Boltzmann equation with a diffusion term
The Boltzmann equation in the critical Besov space Invited

坂本祥太

第30回松山キャンプ 2015.1

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Language：Japanese

Venue：山口大学 Country：Other

The Boltzmann equation in the critical Besov space
Global solutions in the critical Besov space for the non-cutoff Boltzmann equation

坂本祥太

第37回発展方程式若手セミナー 2015.8

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Language：Japanese

Venue：小樽朝里クラッセホテル Country：Other

Global solutions in the critical Besov space for the non-cutoff Boltzmann equation
Global well-posed theory in the critical Besov space for the non cut-off Boltzmann equation Invited International conference

坂本祥太

CAU-Kyoto U. Joint Workshop on Nonlinear PDEs 2015.9

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Language：English

Venue：Seo-gwi-po KAL Hotel, Korea Country：Korea, Republic of

Global well-posed theory in the critical Besov space for the non cut-off Boltzmann equation
非切断Boltzmann 方程式のChemin-Lerner空間における大域解 Invited

坂本祥太

第７回白浜研究集会 2015.12

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Language：Japanese

Venue：紀州・白浜温泉旅館むさし Country：Other

Global solutions to the non-cutoff Boltzmann equation in a Chemin-Lerner space
ベゾフ空間上の拡大写像の転移作用素のスペクトル

坂本祥太

力学系とその関連分野の連携探索 2016.6

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Language：Japanese

Venue：京都大学 Country：Other

Spectra of expanding maps on Besov spaces
Chemin-Lerner空間に初期値をとるボルツマン方程式の時間大域解

坂本祥太

日本数学会2016年度秋季総合分科会 2016.6

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Language：Japanese

Venue：関西大学 Country：Other

Global solution to the Boltzmann equation with initial datum in a Chemin-Lerner space
希薄気体中における粘性摩擦の数理解析 Invited

坂本祥太

第8回白浜研究集会 2016.11

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Venue：紀州・白浜温泉旅館むさし Country：Other
Solution to the Boltzmann equation without angular cutoff in a critical Chemin-Lerner space Invited International conference

坂本祥太

Seminar 2017.8

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Language：English

Venue：The Chinese University of Hong Kong Country：Other

Solution to the Boltzmann equation without angular cutoff in a critical Chemin-Lerner space
重み付きChemin-Lerner 空間上のBoltzmann 方程式の解の構成

坂本祥太

第43回発展方程式研究集会 2017.12

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Language：Japanese

Venue：日本女子大学 Country：Other

Construction of a solution to the Boltzmann equation in a weighed Chemin-Lerner space
Solution to the Boltzmann equation in velocity-weighted Chemin-Lerner type space Invited

坂本祥太

第11 回若手のための偏微分方程式と数学解析 2018.2

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Venue：福岡大学セミナーハウス Country：Other

Solution to the Boltzmann equation in velocity-weighted Chemin-Lerner type space
重み付きChemin-Lerner型空間におけるボルツマン方程式の解

坂本祥太, 段仁軍

日本数学会2018年度年会 2018.3

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Venue：東京大学 Country：Other

A solution to the Boltzmann equation in weighted Chemin-Lerner type space
速度重み付きChemin-Lerner空間におけるボルツマン方程式のコーシー問題の大域解 Invited

坂本祥太

応用数学セミナー 2018.4

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Language：English

Venue：東北大学 Country：Other

Global solution to a Cauchy problem of the Boltzmann equation in a velocity-weighted Chemin-Lerner type space
Global solution to the Boltzmann equation in a velocity-weighted Chemin-Lerner type space Invited International conference

坂本祥太

流体と気体の数理解析 2018.7

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Venue：京都大学 Country：Japan

Global solution to the Boltzmann equation in a velocity-weighted Chemin-Lerner type space
バクテリアの突然変異体の増殖を記述する方程式の運動論的定式化とその確率測度解

坂本祥太

日本数学会2019年度年会 2019.3

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Language：Japanese

Venue：東京工業大学 Country：Other

Kinetic formulation of an equation describing mutation process in bacteria and its probability measure solutions
On recent progress of the Cauchy problem of the Boltzmann equation near Maxwellian Invited

坂本祥太

大阪大学微分方程式セミナー 2019.4

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Language：Japanese

Venue：大阪大学 Country：Other

On recent progress of the Cauchy problem of the Boltzmann equation near Maxwellian
Unique existence of a solution to the Boltzmann equation near Maxwellian in the Wiener space Invited International conference

坂本祥太

RIMS 研究集会偏微分方程式の臨界現象と正則性理論及び漸近解析 2019.5

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Venue：京都 Country：Japan

Unique existence of a solution to the Boltzmann equation near Maxwellian in the Wiener space
Unified theory of construction of global solutions to the Landau and Boltzmann equations Invited

坂本祥太

名古屋微分方程式セミナー 2019.5

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Country：Other

Unified theory of construction of global solutions to the Landau and Boltzmann equations
微生物の突然変異を記述する運動論的モデルの一意大域解と初期確率測度の台の非負性保存 Invited

坂本祥太

第9回岐阜数理科学研究会 2019.9

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Language：Japanese

Venue：飛騨高山まちの博物館研修室 Country：Other
Global solution of the Boltzmann equation without angular cutoff in the Wiener space Invited

坂本祥太

京都大学NLPDEセミナー 2020.6

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Language：Japanese

Country：Other

Global solution of the Boltzmann equation without angular cutoff in the Wiener space
Solutions to the Boltzmann equation without angular cutoff in the Wiener space Invited

坂本祥太

応用解析研究会 2020.10

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Language：Japanese

Country：Other
Global solution to the Boltzmann equation without cutoff on the whole space via $L^1 cap L^p$ approach Invited International conference

Shota Sakamoto

IMS Analysis Seminar 2022.9

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Language：English

Venue：Institute of Mathematical Science, the Chinese University of Hong Kong
Global solution to the Boltzmann equation without cutoff on the whole space via L1∩Lp energy method Invited International conference

Shota Sakamoto

Analysis Seminar 2022.11

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Language：English

Venue：Taipei Country：Taiwan, Province of China
非切断Boltzmann方程式の摂動Cauchy問題の解の一意存在 Invited

坂本祥太

九州大学大学院数理学府数理談話会 2023.5

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Language：Japanese

Country：Other
Global solution to the Boltzmann equation without cutoff on the whole space in (L1∩Lp)k Invited

坂本祥太

応用解析研究会 2023.6

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Language：Japanese

Country：Other

Global solution to the Boltzmann equation without cutoff on the whole space in (L1∩Lp)k
Faster decay of the microscopic part of a solution to the Boltzmann equation Invited International conference

Shota Sakamoto

Kinetic Seminar 2023.9

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非切断Boltzmann方程式の摂動Cauchy問題の解の一意存在 Invited

坂本祥太

九州大学大学院数理学府数理談話会 2023.5

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Language：Japanese Presentation type：Oral presentation (general)

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Global solution to the Boltzmann equation without cutoff on the whole space via L1∩Lp energy method Invited

Shota Sakamoto

Analysis Seminar 2022.11 Institute of Mathematics, Academia Sinica

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Language：English Presentation type：Oral presentation (invited, special)

Venue：Taipei Country：Taiwan, Province of China

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Global solution to the Boltzmann equation without cutoff on the whole space via $L^1 \cap L^p$ approach Invited International coauthorship

Shota Sakamoto

IMS Analysis Seminar 2022.9

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Language：English Presentation type：Public lecture, seminar, tutorial, course, or other speech

Venue：Institute of Mathematical Science, the Chinese University of Hong Kong Country：Hong Kong

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Global solution to the Boltzmann equation without cutoff on the whole space in (L1∩Lp)k Invited

坂本祥太

応用解析研究会 2023.6

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Language：Japanese

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Faster decay of the microscopic part of a solution to the Boltzmann equation Invited

Shota Sakamoto

Kinetic Seminar 2023.9

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Language：English Presentation type：Oral presentation (general)

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全空間上の非切断Boltzmann方程式の時間大域解とその微視的部分の速い減衰 Invited

大阪大学微分方程式セミナー 2024.5

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MISC

希薄気体中における粘性摩擦の数理解析

坂本祥太

第8回白浜研究集会報告集 2017.2

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Language：Japanese
非切断Boltzmann方程式のChemin-Lerner空間における大域解

坂本祥太

第7回白浜研究集会報告集 2016.2

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Language：Japanese
Global solutions in the critical Besov space for the non-cutoff Boltzmann equation

坂本祥太

第37回発展方程式若手セミナー報告集 2015.12

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Language：Japanese

Global solutions in the critical Besov space for the non-cutoff Boltzmann equation
拡散項付きボルツマン方程式の無限エネルギー解

坂本祥太

第6回白浜研究集会報告集 2015.2

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Language：Japanese
Wasserstein 計量を用いたモデルBoltzmann 方程式の解析

坂本祥太

第5回白浜研究集会報告集 2014.2

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Language：Japanese
圧縮性粘性流の初期値問題

坂本祥太

第4回白浜研究集会報告集 2013.2

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Language：Japanese

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Professional Memberships

THE MATHEMATICAL SOCIETY OF JAPAN
THE MATHEMATICAL SOCIETY OF JAPAN

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Committee Memberships

日本数学会 2022年度地方区代議員 Domestic

2022.3 - 2023.2

Academic Activities

Fluids and Maximal Regularity International contribution

Role(s)： Planning, management, etc.

Kyohei Itakura; Shota Sakamoto; Kota Uriya; Shintaro Yagi （ Kyoto University ） 2024.9

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Type：Competition, symposium, etc.

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世話人 International contribution

第41回九州における偏微分方程式研究集会（ Japan ） 2024.1

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Type：Competition, symposium, etc.
Screening of academic papers

Role(s)： Peer review

2023

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Type：Peer review

Number of peer-reviewed articles in foreign language journals：6

Number of peer-reviewed articles in Japanese journals：0

Proceedings of International Conference Number of peer-reviewed papers：0

Proceedings of domestic conference Number of peer-reviewed papers：0
Planning, management, etc., Panel moderator, session chair, etc. International contribution

EAST ASIAN WORKSHOP ON PARTIAL DIFFERENTIAL EQUATIONS IN FLUID DYNAMICS （ Tokyo Institute of Technology Japan ） 2022.1

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Type：Competition, symposium, etc.
実行委員

第7回白浜研究集会（ Japan ） 2015.12

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Type：Competition, symposium, etc.
実行委員

第6回白浜研究集会（ Japan ） 2014.12

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Type：Competition, symposium, etc.

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Research Projects

Regularity of solutions to the non cut-off Boltzmann equation on unbounded domains

Grant number：24K16952 2024.4 - 2028.3

Grants-in-Aid for Scientific Research Grant-in-Aid for Early-Career Scientists

坂本祥太

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Grant type：Scientific research funding

本研究では分子気体運動論の基礎方程式であるボルツマン方程式の解の正則性について明らかにする。特に領域が非有界かつ積分核が非切断型の場合を扱う。この方程式の解は解析性以上の非常に強い正則性を得ることが予想されており、近年の擬微分作用素による線形作用素の明示化により非常に正則性の低い初期条件に対して解の正則化効果が得られることが分かってきた。しかし、これらの結果は全て領域がトーラスの場合に限られており、証明の技法にもこのことが本質的に用いられている。本研究では、解の正則性という局所的性質が領域が全空間や非有界な帯状領域などでも得られることを示す。

CiNii Research
速度特異性を持つ非線形ボルツマン方程式の有界領域における解析

2022 - 2023

住友財団基礎科学研究助成

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Authorship：Principal investigator Grant type：Contract research
Study of properties of solutions to kinetic equations via solution spaces with new structures

Grant number：20K14338 2020.4 - 2024.3

Grants-in-Aid for Scientific Research Grant-in-Aid for Early-Career Scientists

Sakamoto Shota

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Grant type：Scientific research funding

We studied an initial value and initial-boundary value problem of the non cut off Boltzmann equation near the global equilibrium. In particular, solutions are characterized by integrability of their Fourier transform.
In the known results, solution spaces such as Sobolev or Besov spaces that can be embedded into the L infinity space were employed in order to control nonlinear estimates. New solution spaces were utilized so that we can complete estimates without such embedding theorems.

CiNii Research
新たな構造の解空間を用いた運動論方程式の解の諸性質に関する研究

2020 - 2023

Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Early-Career Scientists

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Authorship：Principal investigator Grant type：Scientific research funding
希薄気体中における粘性摩擦の解析学および確率論を用いた研究

2018 - 2019

Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for JSPS Fellows

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Authorship：Principal investigator Grant type：Scientific research funding
希薄気体中における粘性摩擦の解析学および確率論を用いた研究

2018 - 2019

Japan Society for the Promotion of Science Research Fellowships for Young Scientists

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Grant type：Joint research
運動論方程式における解の数理解析

2016 - 2017

Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for JSPS Fellows

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Authorship：Principal investigator Grant type：Scientific research funding
運動論方程式における解の数理解析

2016 - 2017

Japan Society for the Promotion of Science Research Fellowships for Young Scientists

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Grant type：Joint research

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Educational Activities

学部1年生向け微分積分の入門講義と、大学院1年生向け専門科目として偏微分方程式論の基礎講義を担当した。

Class subject

入門微分積分Ⅱ

2023.6 - 2023.8 Summer quarter
非線形解析基礎・演習

2023.4 - 2023.9 First semester
入門微分積分Ⅰ

2023.4 - 2023.6 Spring quarter

FD Participation

2024.2 Role：Participation Title：数理学府FD

Organizer：[Undergraduate school/graduate school/graduate faculty]
2023.8 Role：Participation Title：数理学府FD

Organizer：[Undergraduate school/graduate school/graduate faculty]
2023.4 Role：Participation Title：令和５年度第１回全学ＦＤ（新任教員の研修）The 1st All-University FD (training for new faculty members) in FY2023

Organizer：University-wide

Outline of Social Contribution and International Cooperation activities

一般市民や中学生・高校生を対象とする公開講義やオープンキャンパスでの授業を行った。

Social Activities

数学で遊ぼう(オープンキャンパス企画)

東京工業大学理学院 2020.11

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Type：Other

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数学で遊ぼう(オープンキャンパス企画)

東京工業大学理学院 2020.11

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Audience：General,　Scientific,　Company,　Civic organization,　Governmental agency
高校生のための仙台数学セミナー

Role(s)：Lecturer

公益財団法人川井数理科学財団 2018.8

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Type：Seminar, workshop

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高校生のための仙台数学セミナー

公益財団法人川井数理科学財団 2018.8

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Audience：Infants,　Schoolchildren,　Junior students,　High school students

Type：Seminar, workshop