Vlasov-Maxwell-Boltzmann diffusive limit

Details Vlasov-Maxwell-Boltzmann diffusive limit Vlasov-Maxwell-Boltzmann diffusive limit

2006-01-30

arxiv.org/abs/math/0601740v1

Mathematics

Analysis of PDEs

46 pages

Scientific paper

We study the diffusive expansion for solutions around Maxwellian equilibrium and in a periodic box to the Vlasov-Maxwell-Boltzmann system, the most fundamental model for an ensemble of charged particles. Such an expansion yields a set of dissipative new macroscopic PDE's, the incompressible Vlasov-Navier-Stokes-Fourier system and its higher order corrections for describing a charged fluid, where the self-consistent electromagnetic field is present. The uniform estimate on the remainders is established via a unified nonlinear energy method and it guarantees the global in time validity of such an expansion up to any order.

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