Global Existence and Asymptotic Behavior of Classical Solutions for a 3D Two-Species Keller-Segel-Stokes System with Competitive Kinetics

Abstract

This paper deals with a two-species Keller-Segel-Stokes system with competitive kinetics under homogeneous Neumann boundary conditions in a bounded domain with smooth boundary. The main purpose of this paper is to obtain global existence and stabilization of classical solutions to the system in the 3-dimensional case under the smallness conditions for chemotactic interactions. To this end, this paper develops a maximal Sobolev regularity result for Stokes operator involving a time weighted function, which seems new in the existing literature (see Lemma 2.3 in this paper).