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
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
收藏
页码:287 / 324
页数:38
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