The small-convection limit in a two-dimensional chemotaxis-Navier-Stokes system

被引：50

作者：

Wang, Yulan ^{[1
]}

Winkler, Michael ^{[2
]}

Xiang, Zhaoyin ^{[3
]}

机构：

[1] Xihua Univ, Sch Sci, Chengdu 610039, Sichuan, Peoples R China

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

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

来源：

MATHEMATISCHE ZEITSCHRIFT | 2018年 / 289卷 / 1-2期

关键词：

Chemotaxis; Navier-Stokes; Small-convection limit; Exponential stabilization; KELLER-SEGEL MODELS; LARGE TIME BEHAVIOR; GLOBAL EXISTENCE; NONLINEAR DIFFUSION; WEAK SOLUTIONS; FLUID; STABILIZATION; BOUNDEDNESS; EQUATIONS; DECAY;

D O I：

10.1007/s00209-017-1944-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper deals with an initial-boundary value problem for the chemotaxis-(Navier-)Stokes system in a bounded convex domain with smooth boundary, with and a given smooth potential . It is known that for each and all sufficiently smooth initial data this problem possesses a unique global classical solution . The present work asserts that these solutions stabilize to uniformly with respect to the time variable. More precisely, it is shown that there exist and such that whenever, for all . This result thereby provides an example for a rigorous quantification of stability properties in the Stokes limit process, as frequently considered in the literature on chemotaxis-fluid systems in application contexts involving low Reynolds numbers.

引用

页码：71 / 108

页数：38

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