Existence of Nontrivial Steady State of a Chemotaxis Fluid Coupled System

Abstract

This paper studied a chemotaxis fluid coupled system which models the so-called “chemotactic Boycott effect”. Under certain inhomogeneous boundary conditions, we proved the existence of nontrivial steady state which depends only on one variable of such system in $[0,1]^3.$ A positive lower bound of the oxygen concentration $c$ was also obtained.