Global existence and decay estimates of the Boltzmann equation with frictional force: The general results

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:417

Article

Jiang, Zaihong¹  Wang, Ying² 

[1] Zhejiang Normal Univ, Coll Math Phys & Informat Engn, Jinhua, Peoples R China

[2] City Univ Hong Kong, Dept Math, Kowloon, Hong Kong, Peoples R China

关键词: Boltzmann equation;    Soft potential;    Hard potential;   

DOI  :  10.1016/j.jmaa.2014.02.070

来源: Elsevier

【 摘 要 】

In this paper, we give the existence theory and the optimal time convergence rates of the solutions to the Boltzmann equation with frictional force near a global Maxwellian. We generalize our previous results on the same problem for hard sphere model into both hard potential and soft potential case. The main method used in this paper is the classic energy method combined with some new time velocity weight functions to control the large velocity growth in the nonlinear term for the case of interactions with hard potentials and to deal with the singularity of the cross-section at zero relative velocity for the soft potential case. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free