ASYMPTOTIC ANALYSIS OF THE BOLTZMANN EQUATION WITH VERY SOFT POTENTIALS FROM ANGULAR CUTOFF TO NON-CUTOFF

被引：0

作者：

He, Ling-Bing ^{[1
]}

Yao, Zheng-An ^{[2
]}

Zhou, Yu-Long ^{[2
]}

机构：

[1] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China

[2] Sun Yat Sen Univ, Sch Math, Guangzhou 510275, Peoples R China

来源：

COMMUNICATIONS IN MATHEMATICAL SCIENCES | 2021年 / 19卷 / 02期

关键词：

Boltzmann equation; very soft potential; asymptotic analysis; angular cutoff; angular non-cutoff; short-range interaction; long-range interaction;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Our focus is the Boltzmann equation in a torus under very soft potentials around equilibrium. We analyze the asymptotics of the equation from angular cutoff to non-cutoff. We first prove a refined decay result of the semi-group stemming from the linearized Boltzmann operator. Then we prove the global well-posedness of the equations near equilibrium, refined decay patterns of the solutions. Finally, we rigorously give the asymptotic formula between the solutions to cutoff and non-cutoff equations with an explicit convergence rate.

引用

页码：287 / 324

页数：38

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