Electronic Journal of Differential Equations, 
Vol. 2020 (2020), No. 94, pp. 1-26.

Title: Existence of global weak solutions for a two-dimensional 
       Keller-Segel-Navier-Stokes system with porous medium diffusion 
       and rotational flux
       
Authors: Lingzhu Wang (China West Normal Univ., Nanchong, China)
         Li Xie (Chongqing Normal Univ., Chongqing, China)

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.