Decay estimates of the coupled chemotaxis-fluid equations in R3

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:410

Article

Tan, Zhong¹  Zhang, Xu¹ 

[1] Xiamen Univ, Sch Math Sci, Fujian 361005, Peoples R China

关键词: Navier-Stokes equations;    Chemotaxis;    Chemotaxis-fluid interaction;    Energy method;    Optimal decay rates;    Sobolev interpolation;   

DOI  :  10.1016/j.jmaa.2013.08.008

来源: Elsevier

【 摘 要 】

In this paper, we are concerned with a Chemotaxis-Navier-Stokes model, arising from biology, which is a coupled system of the chemotaxis equations and the viscous incompressible fluid equations with transport and external force. The optimal convergence rates of classical solutions to the Chemotaxis-Navier-Stokes system for small initial perturbation around constant states are obtained by pure energy method under the assumption the initial data belong to (H) over dot(-s) boolean AND H-N , N >= 3 (0 <= s < 3/2). The (H) over dot (0 <= s < 3/2) negative Sobolev norms are shown to be preserved along time evolution. Compared to the result in [5], we obtain the optimal decay rates of the higher-order spatial derivatives of the solutions. (C) 2013 Published by Elsevier Inc.

【 授权许可】

Free