Cauchy problem on the vlasov-fokker-planck equation coupled with the compressible euler equations through the friction force

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Original languageEnglish
Pages (from-to)687-700
Journal / PublicationKinetic and Related Models
Issue number4
Publication statusPublished - Dec 2013
Externally publishedYes


We are concerned with a two-phase ow system consisting of the Vlasov-Fokker-Planck equation for particles coupled to the compressible Euler equations for the uid 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 © American Institute of Mathematical Sciences.

Research Area(s)

  • Convergence rates., Euler equations, Fokker-Planck equations, Stability

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