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Nonnegativity and well-posedness of the regular solution of the magnetized Boltzmann equation. (English) Zbl 1441.35182

Summary: We prove, in this paper, the well-posedness and nonnegativity of the regular solution of the relativistic Boltzmann equation in the presence of a given electromagnetic field, taking as background a Lorentzian space-time which is of type Bianchi I with locally rotational symmetry.

MSC:

35Q20 Boltzmann equations
80A10 Classical and relativistic thermodynamics
76Y05 Quantum hydrodynamics and relativistic hydrodynamics
35B09 Positive solutions to PDEs
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