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

• Main Authors: Lingzhu Wang, Li Xie
• Format: Article
• Language: English
• Published: Texas State University 2020-09-01
• Series: Electronic Journal of Differential Equations
• Subjects: keller-segel-navier-stokes system; nonlinear diffusion; tensor-valued sensitivity; global solution
• Online Access: http://ejde.math.txstate.edu/Volumes/2020/94/abstr.html
• ISSN: 1072-6691

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.