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Global existence and asymptotic stability near equilibrium for the relativistic BGK model. (English) Zbl 1309.35169

Summary: In this paper, the relativistic BGK model is studied. The Jüttner function is presented as the relativistic counterpart of the local Maxwellian equilibrium in the classical case. By linearization around this equilibrium, we obtain a linearized relativistic BGK model and study their time decay at infinity. Finally, existence and asymptotic behavior of close-to-equilibrium solutions of the whole nonlinear relativistic BGK model are proved.

MSC:

35Q75 PDEs in connection with relativity and gravitational theory
35Q35 PDEs in connection with fluid mechanics
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35B35 Stability in context of PDEs
35Q20 Boltzmann equations
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