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Cauchy problem on the Vlasov-Fokker-Planck equation coupled with the compressible Euler equations through the friction force. (English) Zbl 1292.35295
Summary: We are concerned with a two-phase flow system consisting of the Vlasov-Fokker-Planck equation for particles coupled to the compressible Euler equations for the fluid through the friction force. Global well-posedness of the Cauchy problem is established in perturbation framework, and rates of convergence of solutions toward equilibrium, which are algebraic in the whole space and exponential on torus, are also obtained under some additional conditions on initial data. The proof is based on the classical energy estimates.

MSC:
35Q84 Fokker-Planck equations
35Q31 Euler equations
35B35 Stability in context of PDEs
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