Electron. J. Differential Equations, Vol. 2020 (2020), No. 94, pp. 1-26.

Existence of global weak solutions for a two-dimensional Keller-Segel-Navier-Stokes system with porous medium diffusion and rotational flux

Lingzhu Wang, Li Xie

Abstract:
This article concerns a two-dimensional Keller-Segel-Navier-Stokes system with porous medium diffusion and rotational flux describing the coral fertilization. Based on the Gagliardo-Nerenberg inequality and an energy-type argument, we show that, in the context of the nonlinear diffusions of sperm and eggs with index m>1 and l>0, the corresponding initial-boundary value problem possesses at least one global bounded weak solution.

Submitted January 6, 2020. Published September 16, 2020.
Math Subject Classifications: 35A01, 35K55, 35Q92.
Key Words: Keller-Segel-Navier-Stokes system; nonlinear diffusion; tensor-valued sensitivity; global solution.
DOI: 10.58997/ejde.2020.94

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Lingzhu Wang
School of Mathematics & Information
China West Normal University
Nanchong 637002, China
email: lingzhu_math@163.com
Li Xie
School of Mathematical Sciences
Chongqing Normal University
Chongqing 401131, China
email: xieli-520@163.com

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