The Boltzmann equation and nonlinear microlocal analysis

玻尔兹曼方程和非线性微局域分析

• 批准号: 22540187
• 负责人: MORIMOTO Yoshinori
• 金额: $ 2.75万
• 依托单位: Kyoto University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2010
• 资助国家: 日本
• 起止时间: 2010 至 2012
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22540187/
• 关键词: ボルツマン方程式; 衝突積分項; 非切断近似; 平滑効果; 大域解; 安定性; 解の一意性; 測度解; 非線形超局所解析; non-cutoff; 超局所解析; 衝突積分作用素; 時間大域解; 平衡解への安定性; 大域的平衡解

W e considered the Cauchy problem for the Boltzmann equation without angular cutoff approximation. To this Cauchy problem, we showed the structure of solutions, such as, the existence of solutions, the smoothing effect of solutions, the convergence of the equilibrium state, the uniqueness and the non-negativityof solutions, under the physically reasonable assumptions of the collision cross sections. The key ingredient of this study was to give precise lower and upper estimates forthe Boltzmann collision integral operator which contains the singularity with respect to the angular variable between collision particles, by means of the microlocal analysis developed in the theory of linear partial differential equations.

我们考虑了没有角度截止近似的玻尔兹曼方程的柯西问题。对于这个柯西问题，我们在物理上合理的碰撞假设下，展示了解的结构，如解的存在性、解的平滑效应、平衡态的收敛性、解的唯一性和非负性等。横截面。这项研究的关键部分是通过线性偏微分方程理论中发展的微局部分析，对包含碰撞粒子之间角度变量的奇点的玻尔兹曼碰撞积分算子给出精确的下限和上限估计。

项目成果

Hypoelliptic Estimates for a Linear Model of the Boltzmann Equation Without Angular Cutoff

• DOI: 10.1080/03605302.2011.625462
• 发表时间: 2010-12
• 期刊: Communications in Partial Differential Equations
• 影响因子: 1.9
• 作者: N. Lerner;Y. Morimoto;K. Pravda-Starov

Uniqueness of the solution for non-cutoff Boltzmann equation in the whole space

非截止玻尔兹曼方程全空间解的唯一性

• 发表时间: 2010
• 作者: Yiling Lin;Miwako Mishima;Junya Satoh;Masakazu Jimbo;Y.Morimoto
• 通讯作者: Y.Morimoto

Smoothing effect of weak solutions for spatially homogeneous Boltzmann equation

空间齐次玻尔兹曼方程弱解的平滑效应

• 发表时间: 2011
• 作者: Yiling Lin;Miwako Mishima;Masakazu Jimbo;Y.Morimoto
• 通讯作者: Y.Morimoto

Uniqueness of solutions for the non-cutoff Boltzmann equation with soft potential

• DOI: 10.3934/krm.2011.4.919
• 发表时间: 2011-11
• 期刊: Kinetic and Related Models
• 影响因子: 1
• 作者: Radjesvarane Alexandre;Y. Morimoto;S. Ukai;Chao-Jiang Xu;Tong Yang

Global Existence and Full Regularity of the Boltzmann Equation Without Angular Cutoff

• DOI: 10.1007/s00220-011-1242-9
• 发表时间: 2009-12
• 期刊: Communications in Mathematical Physics
• 影响因子: 2.4
• 作者: Radjesvarane Alexandre;Y. Morimoto;S. Ukai;Chao-Jiang Xu;Tong Yang