Global existence of classical solutions for the 2D chemotaxis-fluid system with logistic source

Yina Lin; Qian Zhang; Meng Zhou; Yina Lin; Qian Zhang; Meng Zhou

doi:10.3934/math.2022403

AIMS Mathematics

2022, Volume 7, Issue 4: 7212-7233. doi: 10.3934/math.2022403

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Research article

Global existence of classical solutions for the 2D chemotaxis-fluid system with logistic source

1.
Hebei Key Laboratory of Machine Learning and Computational Intelligence, School of Mathematics and Information Science, Hebei University, Baoding, 071002, China
2.
Department of Software, Hebei Software Institute, Baoding, 071000, China

Received: 12 December 2021 Revised: 17 January 2022 Accepted: 25 January 2022 Published: 09 February 2022
MSC : 35K55, 35Q92, 35Q35, 92C17

In this paper, we consider the incompressible chemotaxis-Navier-Stokes equations with logistic source in spatial dimension two. We first show a blow-up criterion and then establish the global existence of classical solutions to the system for the Cauchy problem under some rough conditions on the initial data.
- chemotaxis,
- Navier-Stokes,
- blow-up,
- classical solutions,
- Cauchy problem
Citation: Yina Lin, Qian Zhang, Meng Zhou. Global existence of classical solutions for the 2D chemotaxis-fluid system with logistic source[J]. AIMS Mathematics, 2022, 7(4): 7212-7233. doi: 10.3934/math.2022403

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Abstract

In this paper, we consider the incompressible chemotaxis-Navier-Stokes equations with logistic source in spatial dimension two. We first show a blow-up criterion and then establish the global existence of classical solutions to the system for the Cauchy problem under some rough conditions on the initial data.

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