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On the Cauchy problem for the relativistic Vlasov-Poisson-Fokker-Planck system. (English) Zbl 1416.35270
Summary: We consider the Cauchy problem for the relativistic Vlasov-Poisson-Fokker-Planck system in the whole space. For perturbative initial data with suitable regularity, we obtain the global classical solutions and prove the exponential time decay rate to the equilibrium around a global relativistic Maxwellian.

MSC:
35Q83 Vlasov equations
35Q84 Fokker-Planck equations
82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics
35A01 Existence problems for PDEs: global existence, local existence, non-existence
76Y05 Quantum hydrodynamics and relativistic hydrodynamics
82D10 Statistical mechanics of plasmas
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