Global existence and large time behavior for a two-dimensional chemotaxis-Navier-Stokes system

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:263

Article

Duan, Renjun¹  Li, Xie^2,3  Xiang, Zhaoyin³ 

[1] Chinese Univ Hong Kong, Dept Math, Hong Kong, Hong Kong, Peoples R China

[2] China West Normal Univ, Coll Math & Informat, Nanchang 637002, Jiangxi, Peoples R China

[3] Univ Elect Sci & Technol China, Sch Math Sci, Chengdu 611731, Sichuan, Peoples R China

关键词: Chemotaxis;    Navier-Stokes;    Global existence;    Convergence;   

DOI  :  10.1016/j.jde.2017.07.015

来源: Elsevier

【 摘 要 】

This paper concerns the coupled chemotaxis-Navier-Stokes system in the two-dimensional setting. Such a system was proposed in [19] to describe the collective effects arising in bacterial suspensions in fluid drops. Under some basic assumptions on the parameter functions chi(.), K(.) and the potential function phi, which are consistent with those used by the experimentalists but weaker than those appeared in the known mathematical works, we establish the global existence of weak solutions and classical solutions for both the Cauchy problem and the initial-boundary value problem supplemented with some initial data. For the initial-boundary value problem, we also assert that the solution converges in large time to the spatially homogeneous equilibrium ((n(0)) over bar ,0,0), 0, 0) with (n(0)) over bar := 1/vertical bar Omega vertical bar integral Omega n(0)(x)dx. Our results also show that the large diffusion of the cell density or the chemical concentration can rule out the finite-time blow-up even though the Navier Stokes fluid is included. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free