Global classical solutions close to equilibrium to the Vlasov-Fokker-Planck-euler system

José A. Carrillo, Renjun Duan, Ayman Moussa

Research output: Contribution to journalArticleResearchpeer-review

48 Citations (Scopus)

Abstract

We are concerned with the global well-posedness of a two-phase flow system arising in the modelling of fluid-particle interactions. This sys- tem consists of the Vlasov-Fokker-Planck equation for the dispersed phase (particles) coupled to the incompressible Euler equations for a dense phase (fluid) through the friction forcing. Global existence of classical solutions to the Cauchy problem in the whole space is established when initial data is a small smooth perturbation of a constant equilibrium state, and moreover an algebraic rate of convergence of solutions toward equilibrium is obtained under additional conditions on initial data. The proof is based on the macro-micro decomposition and Kawashima's hyperbolic-parabolic dissipation argument. This result is generalized to the periodic case, when particles are in the torus, improving the rate of convergence to exponential. © American Institute of Mathematical Sciences.
Original languageEnglish
Pages (from-to)227-258
JournalKinetic and Related Models
Volume4
DOIs
Publication statusPublished - 1 Mar 2011

Keywords

  • Global well-posedness
  • Rate of convergence
  • Two-phase flow system

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