Global well-posedness for the Fokker-Planck-Boltzmann equation in Besov-Chemin-Lerner type spaces

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:260

Article

Liu, Zhengrong¹  Tang, Hao² 

[1] S China Univ Technol, Dept Math, Guangzhou 510641, Guangdong, Peoples R China

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

关键词: Fokker-Planck-Boltwnnn equation;    Hard potential;    Cutoff assumption;    Cauchy problem;    Littlewood Paley theory;   

DOI  :  10.1016/j.jde.2016.02.031

来源: Elsevier

【 摘 要 】

In this paper, motivated by [16], we use the Littlewood Paley theory to establish some estimates on the nonlinear collision term, which enable us to investigate the Cauchy problem of the Fokker Planck Boltzmann equation. When the initial data is a small perturbation of the Maxwellian equilibrium state, under the Grad's angular cutoff assumption, the unique global solution for the hard potential case is obtained in the Besov-Chemin-Lemer 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 obtain the uniform stability of the 'dependence on the initial data. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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