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Global boundedness of solutions to a chemotaxis-fluid system with singular sensitivity and logistic source

Global boundedness of solutions to a chemotaxis-fluid system with singular sensitivity and logistic source

Authors :
Bin Liu
Guoqiang Ren
Source :
Communications on Pure & Applied Analysis. 19:3843-3883
Publication Year :
2020
Publisher :
American Institute of Mathematical Sciences (AIMS), 2020.

Abstract

In this paper, we investigate the chemotaxis-fluid system with singular sensitivity and logistic source in bounded convex domain with smooth boundary. We present the global existence of very weak solutions under appropriate regularity assumptions on the initial data. Then, we show that system possesses a global bounded classical solution. Finally, we present a unique globally bounded classical solution for a fluid-free system. In addition, the asymptotic behavior of the solutions is studied, and our results generalize and improve some well-known results in the literature, and partially results are new.

Details

ISSN :
15535258
Volume :
19
Database :
OpenAIRE
Journal :
Communications on Pure & Applied Analysis
Accession number :
edsair.doi...........e04d1cf2ec8da9b144f29f2aa6a2d6ac
Full Text :
https://doi.org/10.3934/cpaa.2020170