Archive for Rational Mechanics and Analysis

, Volume 194, Issue 2, pp 531–584

Vlasov–Maxwell–Boltzmann Diffusive Limit


DOI: 10.1007/s00205-008-0169-6

Cite this article as:
Jang, J. Arch Rational Mech Anal (2009) 194: 531. doi:10.1007/s00205-008-0169-6


Inspired by the work (Bastea et al. in J Stat Phys 1011087–1136, 2000) for binary fluids, 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 PDEs, 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.

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Institute for Advanced studyPrincetonUSA
  2. 2.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA