Global solvability and stabilization in a three-dimensional coral fertilization model involving the Navier-Stokes equations

Abstract

This paper deals with a coral fertilization model involving the Navier-Stokes equations. It is proved that an associated initial-boundary value problem with no-flux, Dirichlet boundary conditions in a three-dimensional smoothly bounded domain admits a globally defined weak solution for any appropriately regular initial data whenevermax⁡{‖c0‖∞,‖m0‖∞}<π2χ, where χ is the chemotaxis sensitivity and m0,c0 are initial density of unfertilized eggs and initial concentration of the chemical expelled by the eggs, respectively. Moreover, it is showed that the obtained solutions stabilize to a certain constant equilibrium.