Large Time Periodic Solution And Asymptotic Behavior To Chemotaxis-stokes Models

Firstly,we investigate the existence of the time periodic solutions of the following problem（?） which Q=Ω×R+ and Ω（?） R3 is a bounded domain with （?）Ω∈ C2+α（0<α<1）.Here we mainly deal with the existence of large time periodic solution of the coupled chemotaxisfluid model with logistic growth term in spatial dimension N=3.Besides,we also prove that if the time periodic source g and the potential force f belong to Cα,α/2,the solution is also a classical solution.Next,we consider asymptotic behavior to the following model（where p>2）,（?）in a bounded domain Ω of R3 with zero-flux boundary conditions and no-slip boundary condition.Similar to the study for the chemotaxis-Stokes system with porous medium diffusion,it is also a challenging problem to find an optimal p-value（p≥ 2）which ensures that the solution is global bounded.In particular,the closer the value of p is to 2,the more difficult the study becomes.In this thesis,we will prove the large time behavior of solutions and show the weak solutions converge to the spatially homogeneous steady state（n0,0,n0,0）.Comparing with the chemotaxis-fluid system with porous medium diffusion,the present convergence of n is proved in the sense of L∞-norm,not only in Lp-norm or weak-*topology.