Large time behavior in a three-dimensional degenerate chemotaxis-Stokes system modeling coral fertilization

This paper is concerned with the effects of nonlinear diffusion on global solvability and stabilization in a variety of models which generalizes the following prototype with a given function phi is an element of W-2,W-infinity(Omega), where Omega subset of R-3 is a general bounded domain with smooth boundary. Based on an energy-type argument combined with maximal Sobolev regularity theory, we conclude that if an associated initial-boundary value problem admits at least one globally bounded weak solution which stabilizes toward the spatial homogeneous equilibrium (n(infinity), rho(infinity), rho(infinity), 0) in the sense that (C) 2020 Elsevier Inc. All rights reserved.