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The Navier-Stokes-Vlasov-Fokker-Planck system near equilibrium

Abstract : This paper is concerned with a system that couples the incompressible Navier-Stokes equations to the Vlasov-Fokker-Planck equation. Such a system arises in the modeling of sprays, where a dense phase interacts with a disperse phase. The coupling arises from the Stokes drag force exerted by a phase on the other. We study the global-in-time existence of classical solutions for data close to an equilibrium. We investigate further regularity properties of the solutions as well as their long time behavior. The proofs use energy estimates and the hypoelliptic structure of the system.
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Contributor : Thierry Goudon <>
Submitted on : Saturday, May 16, 2009 - 12:37:21 AM
Last modification on : Thursday, April 15, 2021 - 3:31:39 AM
Long-term archiving on: : Thursday, June 10, 2010 - 11:12:12 PM


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  • HAL Id : inria-00384364, version 1


Thierry Goudon, Lingbing He, Ayman Moussa, Ping Zhang. The Navier-Stokes-Vlasov-Fokker-Planck system near equilibrium. 2009. ⟨inria-00384364⟩



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