Global existence of weak solutions for Navier-Stokes-BGK system

被引：13

作者：

Choi, Young-Pil ^{[1
]}

Yun, Seok-Bae ^{[2
]}

机构：

[1] Yonsei Univ, Dept Math, 50 Yonsei Ro, Seoul 03722, South Korea

[2] Sungkyunkwan Univ, Dept Math, Suwon 440746, South Korea

来源：

NONLINEARITY | 2020年 / 33卷 / 04期

基金：

新加坡国家研究基金会;

关键词：

Vlasov equation; BGK model; incompressible Navier-Stokes equations; spray models; global existence of weak solutions; SEMI-LAGRANGIAN SCHEME; KINETIC-EQUATIONS; CAUCHY-PROBLEM; CLASSICAL-SOLUTIONS; EULER EQUATIONS; MODEL; VLASOV; LIMIT; MOMENTS; CONVERGENCE;

D O I：

10.1088/1361-6544/ab6c38

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the global well-posedness of a coupled system of kinetic and fluid equations. More precisely, we establish the global existence of weak solutions for Navier-Stokes-BGK system consisting of the BGK model of Boltzmann equation and incompressible Navier-Stokes equations coupled through a drag forcing term. This is achieved by combining weak compactness of the particle interaction operator based on Dunford-Pettis theorem, strong compactness of macroscopic fields of the kinetic part relied on velocity averaging lemma and a high order moment estimate, and strong compactness of the fluid part by Aubin-Lions lemma.

引用

页码：1925 / 1955

页数：31

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