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Vlasov–Maxwell–Boltzmann Diffusive Limit

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Abstract

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.

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  1. Juhi Jang

    Present address: Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY, 10012, USA

Authors and Affiliations

  1. Institute for Advanced study, Princeton, USA

    Juhi Jang

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  1. Juhi Jang
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Correspondence to Juhi Jang.

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Communicated by T.-P. Liu

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Jang, J. Vlasov–Maxwell–Boltzmann Diffusive Limit. Arch Rational Mech Anal 194, 531–584 (2009). https://doi.org/10.1007/s00205-008-0169-6

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  • DOI: https://doi.org/10.1007/s00205-008-0169-6

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