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）
Title
Associate Professor
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。
External link
Research History
-
Kyushu University Faculty of Mathematics Associate Professor
2023.4 - Present
Country：Japan
-
Tokyo Institute of Technology Department of Mathematics, School of Science Assistant Professor
2020.4 - 2023.3
Country：Japan
Research Interests・Research Keywords
-
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：Kinetic equations
Keyword：Kinetic equations
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
-
Global Mild Solutions of the Landau and Non‐Cutoff Boltzmann Equations Reviewed
2020.6
-
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
-
Shota Sakamoto
Journal of Mathematical Analysis and Applications 507 ( 1 ) 125771 - 125771 2022.3 （ ISSN:0022-247X ）
-
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 ）
-
Spectra of expanding maps on Besov spaces Reviewed
Yushi Nakano, Shota Sakamoto
Discrete and Continuous Dynamical Systems 39 ( 4 ) 1779 - 1797 2019.4
-
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
-
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
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
-
Global solutions to the Boltzmann equation without angular cut-off that are characterized by integrability of their Fourier transform Invited
2023.12
-
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
-
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
-
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
-
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
-
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
-
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
-
Solution to the Boltzmann equation without cutoff in $(L^1cap L^p)_k$ Invited International conference
Shota Sakamoto
ICIAM 2023 2023.8
-
Solution to the Boltzmann equation without cutoff in $(L^1\cap L^p)_k$ Invited
Shota Sakamoto
ICIAM 2023 2023.8
-
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
-
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
-
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
-
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
-
Shota Sakamoto
Rigorous Statistical Mechanics and Related Topics 2022.11 RIMS, Kyoto University
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
Some remarks on the homogeneous Boltzmann equation with the fractional Laplacian term Invited International conference
Doctorial Forum of Mathematics between Fudan and Kyoto Universities 2014.11
-
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
-
The Boltzmann equation in the critical Besov space Invited
2015.1
-
Global solutions in the critical Besov space for the non-cutoff Boltzmann equation
2015.8
-
Global well-posed theory in the critical Besov space for the non cut-off Boltzmann equation Invited International conference
CAU-Kyoto U. Joint Workshop on Nonlinear PDEs 2015.9
-
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
-
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
-
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
-
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
-
Solution to the Boltzmann equation without angular cutoff in a critical Chemin-Lerner space Invited International conference
Seminar 2017.8
-
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
-
Solution to the Boltzmann equation in velocity-weighted Chemin-Lerner type space Invited
2018.2
-
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
-
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
-
Global solution to the Boltzmann equation in a velocity-weighted Chemin-Lerner type space Invited International conference
2018.7
-
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
-
On recent progress of the Cauchy problem of the Boltzmann equation near Maxwellian Invited
2019.4
-
Unique existence of a solution to the Boltzmann equation near Maxwellian in the Wiener space Invited International conference
2019.5
-
Unified theory of construction of global solutions to the Landau and Boltzmann equations Invited
2019.5
-
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
-
Global solution of the Boltzmann equation without angular cutoff in the Wiener space Invited
2020.6
-
Solutions to the Boltzmann equation without angular cutoff in the Wiener space Invited
2020.10
-
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
-
Global solution to the Boltzmann equation without cutoff on the whole space via L1∩Lp energy method Invited International conference
2022.11
-
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
-
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
-
Faster decay of the microscopic part of a solution to the Boltzmann equation Invited International conference
Shota Sakamoto
Kinetic Seminar 2023.9
-
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
-
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
-
Global solution to the Boltzmann equation without cutoff on the whole space in (L1∩Lp)k Invited
2023.6
-
Faster decay of the microscopic part of a solution to the Boltzmann equation Invited
Shota Sakamoto
Kinetic Seminar 2023.9
-
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
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
-
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
-
Global solutions in the critical Besov space for the non-cutoff Boltzmann equation
2015.12
-
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
-
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
-
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
Professional Memberships
-
THE MATHEMATICAL SOCIETY OF JAPAN
-
THE MATHEMATICAL SOCIETY OF JAPAN
Committee Memberships
-
日本数学会 2022年度地方区代議員 Domestic
2022.3 - 2023.2
Academic Activities
-
世話人 International contribution
第41回 九州における偏微分方程式研究集会 （ 九州大学 西新プラザ ） 2024.1
-
Screening of academic papers
Role(s)： Peer review
2023
-
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
-
実行委員
第7回白浜研究集会 （ 白浜 ） 2015.12
-
実行委員
第6回白浜研究集会 （ 白浜 ） 2014.12
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
Grant type：Scientific research funding
-
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
Authorship：Principal investigator Grant type：Contract 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
日本学術振興会 科学研究費助成事業 若手研究
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
日本学術振興会 科学研究費助成事業 特別研究員奨励費
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
日本学術振興会 特別研究員
Grant type：Joint research
-
運動論方程式における解の数理解析
2016 - 2017
日本学術振興会 科学研究費助成事業 特別研究員奨励費
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
日本学術振興会 特別研究員
Grant type：Joint research
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
-
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
-
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
-
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