Communications in Mathematical Sciences

Volume 21 (2023)

Number 6

The global generalized solution of the chemotaxis-Navier–Stokes system with logistic source

Pages: 1549 – 1568

DOI: https://dx.doi.org/10.4310/CMS.2023.v21.n6.a5

Authors

Dandan Ding (School of Mathematical Sciences, Xiamen University, Xiamen, Fujian, China)

Zhong Tan (School of Mathematical Sciences, Xiamen University, Xiamen, Fujian, China; and Shenzhen Research Institute of Xiamen University, Shenzhen, China)

Zhonger Wu (School of Mathematical Sciences, Xiamen University, Xiamen, Fujian, China)

Abstract

In this paper, we consider the initial boundary value problem of the chemotaxis-Navier–Stokes system with low regularity, and we show that the system has a global generalized solution, which was first introduced by M. Winkler [$\href{https://doi.org/10.1137/140979708}{26}$].

Keywords

chemotaxis Navier–Stokes system, logistic source, global generalized solution, low regularity

2010 Mathematics Subject Classification

35A01, 35K51, 35Q92, 92C17

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This work was supported by the National Natural Science Foundation of China (Grant Nos. 12231016 and 12071391), and by the Guangdong Basic and Applied Basic Research Foundation (Grant No. 2022A1515010860).

Received 5 May 2022

Accepted 19 November 2022

Published 22 September 2023