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Global weak solutions to the relativistic BGK equation. (English) Zbl 1437.35659

Summary: In this paper, the global existence of weak solutions to the relativistic BGK model for the relativistic Boltzmann equation is analyzed. The proof relies on the strong compactness of the density, velocity, and temperature under minimal assumptions on the control of some moments of the initial condition together with the initial entropy.

MSC:

35Q75 PDEs in connection with relativity and gravitational theory
35Q20 Boltzmann equations
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
82C40 Kinetic theory of gases in time-dependent statistical mechanics
35D30 Weak solutions to PDEs
35A01 Existence problems for PDEs: global existence, local existence, non-existence
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References:

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