Asymptotic behavior of classical solutions of a three-dimensional Keller-Segel-Navier-Stokes system modeling coral fertilization (Q2182766)

A system of six parabolic equations modeling coral fertilization is studied in three-dimensional domains. These are: a chemotactic type equation for the evolution of the density of sperms, linear equation for diffusion of eggs, equation for diffusion of a chemoattractant, and equations for the fluid velocity. The chemotactic sensitivity is a general tensor valued function which is assumed to be bounded. The asymptotic stability of homogeneous steady states in this Keller-Segel-Navier-Stokes system is shown under some regularity and size conditions imposed on the initial values.