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.

Keywords

Chemotaxis / Navier-Stokes equations / steady state / mixed boundary conditions