Global existence and stabilization in a degenerate chemotaxis-Stokes system with mildly strong diffusion enhancement

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:264

Article

Winkler, Michael¹ 

[1] Univ Paderborn, Inst Math, D-33098 Paderborn, Germany

关键词: Chemotaxis;    Stokes;    Nonlinear diffusion;    Boundedness;    Stabilization;    Maximal Sobolev regularity;   

DOI  :  10.1016/j.jde.2018.01.027

来源: Elsevier

【 摘 要 】

A class of chemotaxis-Stokes systems generalizing the prototype { n(t) + u center dot del n = del center dot (n(m-1)del n) - del center dot (n del c), c(t) + u center dot del c = Delta c - nc, ut + del P = Delta u + n del phi, del center dot u = 0, is considered in bounded convex three-dimensional domains, where phi is an element of W-2,W-infinity (Omega) is given. The paper develops an analytical approach which consists in a combination of energy-based arguments and maximal Sobolev regularity theory, and which allows for the construction of global bounded weak solutions to an associated initial-boundary value problem under the assumption that m > 9/8. Moreover, the obtained solutions are shown to approach the spatially homogeneous steady state (1/|Omega| integral(Omega) n(0), 0, 0) in the large time limit. This extends previous results which either relied on different and apparently less significant energy- type structures, or on completely alternative approaches, and thereby exclusively achieved comparable results under hypotheses stronger than (0.1). (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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