The Study Of A Three-Dimensional Chemotaxis-Fluid System With Rotational Flux

This paper is concerned with the following chemotaxis-Stokes system under no-flux boundary conditions in a bounded domain ?(?)R3 with smooth boundary. Here S=(sij)i,j?{1,2,3} is a chemotactic sensitivity tensor which satisfies Sij,?C2 (?×[0?) × [0, ?)), i, j?{1,2,3} and S(x,n,c)|?Cs(1+n)-?, ?>0, (x,n,c)??× [0,?)×[0,?), for some constant Cs>0.This thesis consists of four parts:In Chapter 1, we briefly introduce the biological background and the development status of the related studies.In Chapter 2, we first introduce our problem and state the main results, then we give some preliminaries, which include some lemmas and the boundary regularization of system.In Chapter 3, we prove the boundedness of the solution to system(*). The main approach is to establish some a priori estimates.Chapter 4, we analysis the stability of the solution. We proved that the classical solution trends to the steady state of the problem as the time trends to infinity.