TIME PERIODIC SOLUTION TO A COUPLED CHEMOTAXIS-FLUID MODEL WITH POROUS MEDIUM DIFFUSION

This paper is concerned with the time periodic problem to a cou- pled chemotaxis-fluid model with porous medium diffusion Delta n(m) The global existence of solutios for the initial and boundary value problem of this model have been studied by many authors, and in particular, the global solvability is established for m > 6/5 in dimension 3. Here, taking advantage of a double-level approximation scheme, we establish the existence of uniformly bounded time periodic solution for any m >= 6/5 and any large periodic source g(x , t). In particular, the energy estimates techniques we used also applicable to the proof of global existence of the initial-boundary value problem, and one can supply the existence of global solutions for m = 6/5 by this method.