ON THE CAUCHY PROBLEM FOR THE BOLTZMANN EQUATION IN CHEMIN-LERNER TYPE SPACES

被引：3

作者：

Tang, Hao ^{[1
]}

Liu, Zhengrong ^{[1
]}

机构：

[1] S China Univ Technol, Dept Math, Guangzhou 510640, Guangdong, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2016年 / 36卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Boltzmann equation; Cauchy problem; hard potential; angular cutoff assumption; Littlewood-Paley theory; WHOLE SPACE; CLASSICAL-SOLUTIONS; GLOBAL EXISTENCE; ANGULAR CUTOFF; WELL-POSEDNESS; SYSTEM; STABILITY; ENTROPY;

D O I：

10.3934/dcds.2016.36.2229

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, motivated by [13], we use the Littlewood-Paley theory to investigate the Cauchy problem of the Boltzmann equation. When the initial data is a small perturbation of an equilibrium state, under the Grad's angular cutoff assumption, we obtain the unique global strong solution to the Boltzmann equation for the hard potential case in the Chemin-Lerner type spaces C([0, infinity); (L) over tilde (2)(xi)(B-2,r(s))) with 1 <= r <= 2 and s > 3/2 or s = 3/2 and r = 1. Besides, we also prove the Lipschitz continuity of the solution map. Our results extend some previous works on the Boltzmann equation in Sobolev spaces.

引用

页码：2229 / 2256

页数：28

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