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Applicable Analysis
An International Journal
Volume 101, 2022 - Issue 3
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Articles

The rates of convergence for the chemotaxis-Navier–Stokes equations in a strip domain

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Pages 952-969 | Received 27 Aug 2019, Accepted 29 Apr 2020, Published online: 14 May 2020
 

ABSTRACT

In this paper, we study the long-time behavior of the chemotaxis-Navier–Stokes system tn+un=λΔn(χ(c)nc),tc+uc=μΔcf(c)n,tu+uu+P=ζΔunφ,u=0,t>0,xΩ posed in a strip domain Ω:=R2×[0,1]R3. In Peng-Xiang (Math. Models Methods Appl. Sci., 28 (2018), 869-920), the authors have established the global existence of strong solutions to this system with non-flux boundary conditions for n and c and non-slip boundary conditions for u. Our main purpose is to establish the time-decay rates for such solutions. This will be done by using the anisotropic Lp interpolation and the iterative techniques.

AMS (2000) Subject Classifications:

Acknowledgements

The authors are very grateful to the reviewers for their detailed comments and valuable suggestions, which greatly improved the manuscript. Hongxia Lin acknowledges support by the NSF of China under Grant 11701049, the China Postdoctoral Science Foundation under Grant 2017M622989, and the Scientific fund of the Education Department of Sichuan Province under Grant 18ZB0069.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Hongxia Lin acknowledges support by the NSF of China [grant number 11701049], the China Postdoctoral Science Foundation [grant number 2017M622989], and Scientific Research Foundation of the Education Department of Sichuan Province [grant number 18ZB0069].

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