Kyushu University [Sakamoto Shota (Associate Professor) Faculty of Mathematics, Division of Analysis]

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Researcher information

Sakamoto Shota
Associate Professor
Division of Analysis
Faculty of Mathematics
Last modified date：2024.04.05

Graduate School

Department of Mathematics
Graduate School of Mathematics

Undergraduate School

Department of Mathematics
School of Sciences

Homepage

Country of degree conferring institution (Overseas)

Field of Specialization

Total Priod of education and research career in the foreign country

Research

Research Interests

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
2016.04.

Academic Activities

Reports

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Papers

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1.	Renjun Duan, Shota Sakamoto, Yoshihiro Ueda, An (oldsymbol{L^1_{k}cap L^{p}_{k } }) Approach for the Non-Cutoff Boltzmann Equation in (oldsymbol{mathbb{R}^3}), SIAM Journal on Mathematical Analysis, 10.1137/22m1533232, 56, 1, 762-800, 2024.01.
2.	Yoshinori Morimoto, Shota Sakamoto, Global solutions in the critical Besov space for the non-cutoff Boltzmann equation, JOURNAL OF DIFFERENTIAL EQUATIONS, 10.1016/j.jde.2016.06.017, 261, 7, 4073-4134, 2016.10, 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..
3.	Renjun Duan, Shuangqian Liu, Shota Sakamoto, Robert M. Strain, Global Mild Solutions of the Landau and Non‐Cutoff Boltzmann Equations, Communications on Pure and Applied Mathematics, 10.1002/cpa.21920, 2020.06, 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。.

Presentations

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

Membership in Academic Society

THE MATHEMATICAL SOCIETY OF JAPAN

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