Boundedness and asymptotic behavior to a chemotaxis-fluid system with singular sensitivity and logistic source

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:484

Article

Wu, Jie¹  Natal, Helio¹ 

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

关键词: Chernotaxis-fluid;    Singular sensitivity;    Logistic source;    Asymptotic behavior;   

DOI  :  10.1016/j.jmaa.2019.123748

来源: Elsevier

【 摘 要 】

In this paper, we consider the following chemotaxis-fluid model with singular sensitivity and logistic source {n(t) + u.del n = Delta n - chi del. (n/c del c) + rn- mu n(k), x is an element of Omega, t > 0, c(t) + u.del c = Delta c-c + n, x is an element of Omega, t > 0, u(t) + lambda (u.del)u = Delta u + del P + n del phi, x is an element of Omega, t > 0, del.u = 0, x is an element of Omega, t > 0 in a bounded domain Omega subset of R-N (N = 2, 3) with smooth boundary partial derivative Omega. Under the non-flux boundary conditions for n and c, and the non-slip boundary condition for u, we establish the global boundedness and the time-decay rates of the classical solutions for any k > 1 provided that chi satisfies suitable restrictions. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

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