The Vlasov-Maxwell-Boltzmann System Near Maxwellians in the Whole Space with Very Soft Potentials

被引：20

作者：

Duan, Renjun ^{[1
]}

Lei, Yuanjie ^{[2
]}

Yang, Tong ^{[3
,4
]}

Zhao, Huijiang ^{[5
,6
]}

机构：

[1] Chinese Univ Hong Kong, Dept Math, Shatin, Hong Kong, Peoples R China

[2] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Peoples R China

[3] Jinan Unv, Dept Math, Guangzhou, Peoples R China

[4] City Univ Hong Kong, Dept Math, Tat Chee Ave, Kowloon, Hong Kong, Peoples R China

[5] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China

[6] Wuhan Univ, Computat Sci Hubei Key Lab, Wuhan 430072, Peoples R China

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2017年 / 351卷 / 01期

基金：

中国国家自然科学基金;

关键词：

POISSON-LANDAU SYSTEM; NEGATIVE SOBOLEV SPACES; ANGULAR CUTOFF; CLASSICAL-SOLUTIONS; PERIODIC BOX; EQUATION; DECAY; STABILITY; REGULARITY; PLASMA;

D O I：

10.1007/s00220-017-2844-7

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Since the work by Guo (Invent Math 153(3):593-630, 2003), it has remained an open problem to establish the global existence of perturbative classical solutions around a global Maxwellian to the Vlasov-Maxwell-Boltzmann system with the whole range of soft potentials. This ismainly due to the complex structure of the system, in particular, the degenerate dissipation at large velocity, the velocity-growth of the nonlinear term induced by the Lorentz force, and the regularity-loss of the electromagnetic fields. This paper solves this problem in the whole space provided that initial perturbation has sufficient regularity and velocity-integrability.

引用

页码：95 / 153

页数：59

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