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The Vlasov–Maxwell–Boltzmann System in the Whole Space

Communications in Mathematical Physics volume 268, pages 543–567 (2006)Cite this article

Abstract

The Vlasov–Maxwell–Boltzmann system is one of the most fundamental models to describe the dynamics of dilute charged particles, where particles interact via collisions and through their self-consistent electromagnetic field. We prove existence of global in time classical solutions to the Cauchy problem near Maxwellians.

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Authors and Affiliations

  1. Department of Mathematics, Harvard University, Cambridge, MA, 02138, USA

    Robert M. Strain

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  1. Robert M. Strain
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Correspondence to Robert M. Strain.

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Communicated by H.-T. Yau

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Strain, R.M. The Vlasov–Maxwell–Boltzmann System in the Whole Space. Commun. Math. Phys. 268, 543–567 (2006). https://doi.org/10.1007/s00220-006-0109-y

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  • DOI: https://doi.org/10.1007/s00220-006-0109-y

Keywords

  • Cauchy Problem
  • Boltzmann Equation
  • Global Existence
  • Sobolev Inequality
  • Temporal Derivative