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- Title
The Vlasov-Maxwell-Boltzmann System Near Maxwellians in the Whole Space with Very Soft Potentials.
- Authors
Duan, Renjun; Lei, Yuanjie; Yang, Tong; Zhao, Huijiang
- Abstract
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 is mainly 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.
- Subjects
MAXWELL-Boltzmann function; CLASSICAL solutions (Mathematics); DEGENERATE perturbation theory; NONLINEAR analysis; ELECTROMAGNETIC fields; LORENTZ force
- Publication
Communications in Mathematical Physics, 2017, Vol 351, Issue 1, p95
- ISSN
0010-3616
- Publication type
Article
- DOI
10.1007/s00220-017-2844-7