Existence and decay of global smooth solutions to the coupled chemotaxis-fluid model

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:427

Article

Ye, Xia

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

DOI  :  10.1016/j.jmaa.2015.02.023

来源: Elsevier

【 摘 要 】

In this paper, we consider a coupled chemotaxis fluid model in R-3, which describes the so-called chemotaxis Boycott effect arising from the interplay of chemotaxis and diffusion of nutrients or signaling chemicals in bacterial suspensions. It is shown that the Cauchy problem has a unique global-in-time solution (n, c, u)(x, t) on R-3 x (0, infinity), provided the invariant initial norm parallel to(u(0), del(c0))parallel to(L3) + parallel to n(0)parallel to(L3/2) is suitably small, or the diffusion coefficients of cells, substrate and fluid (i.e. lambda, nu, mu) are large enough. We also show that the invariant norm parallel to(u, del c)(t)parallel to(3)(L3) + parallel to n(t)parallel to(3/2)(L3/2) is monotone decreasing in t for all t >= 0. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free