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Journal Articles SIAM Journal on Mathematical Analysis Year : 2010

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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Dates and versions

inria-00384364 , version 1 (16-05-2009)

Identifiers

Cite

Thierry Goudon, Lingbing He, Ayman Moussa, Ping Zhang. The Navier-Stokes-Vlasov-Fokker-Planck system near equilibrium. SIAM Journal on Mathematical Analysis, 2010, 42 (5), ⟨10.1137/090776755⟩. ⟨inria-00384364⟩
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