EXISTENCE OF SMOOTH SOLUTIONS TO COUPLED CHEMOTAXIS-FLUID EQUATIONS

被引：180

作者：

Chae, Myeongju ^{[1
]}

Kang, Kyungkeun ^{[2
]}

Lee, Jihoon ^{[3
]}

机构：

[1] Hankyong Natl Univ, Dept Appl Math, Ansung, South Korea

[2] Yonsei Univ, Dept Math, Seoul 120749, South Korea

[3] Sungkyunkwan Univ, Dept Math, Suwon, South Korea

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2013年 / 33卷 / 06期

基金：

新加坡国家研究基金会;

关键词：

Chemotaxis-fluid equations; Keller-Segel; Navier-Stokes system; global solutions; energy estimates; MODEL;

D O I：

10.3934/dcds.2013.33.2271

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a system coupling the parabolic-parabolic Keller-Segel equations to the in- compressible Navier-Stokes equations in spatial dimensions two and three. We establish the local existence of regular solutions and present some blow-up criteria. For two dimensional Navier-Stokes-Keller-Segel equations, regular solutions constructed locally in time are, in reality, extended globally under some assumptions pertinent to experimental observation in [20] on the consumption rate and chemotactic sensitivity. We also show the existence of global weak solutions in spatially three dimensions with rather restrictive consumption rate and chemotactic sensitivity.

引用

页码：2271 / 2297

页数：27

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