THE NAVIER-STOKES-VLASOV-FOKKER-PLANCK SYSTEM NEAR EQUILIBRIUM

被引：74

作者：

Goudon, Thierry ^{[1
]}

He, Lingbing ^{[2
]}

Moussa, Ayman ^{[3
]}

Zhang, Ping ^{[4
]}

机构：

[1] INRIA Res Ctr Lille Nord Europe, Project Team SIMPAF, F-59658 Villeneuve Dascq, France

[2] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China

[3] ENS Cachan, CMLA, PRES UniverSud, CNRS, F-94230 Cachan, France

[4] Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2010年 / 42卷 / 05期

基金：

中国博士后科学基金;

关键词：

fluid-particle flows; hypocoercivity; hypoelliptic operator; ASYMPTOTIC ANALYSIS; CLASSICAL-SOLUTIONS; HYDRODYNAMIC LIMIT; GLOBAL EQUILIBRIUM; SMOOTH SOLUTION; PARTICLES; REGULARITY; EQUATIONS; TREND; MODEL;

D O I：

10.1137/090776755

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 hypocoercive/hypoelliptic structure of the system.

引用

页码：2177 / 2202

页数：26

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