Bounded weak and strong time periodic solutions to a three-dimensional chemotaxis-Stokes model with porous medium diffusion

Abstract

In this paper, we study the time periodic problem to a three-dimensional chemotaxis-Stokes model with porous medium diffusion Δnm and inhomogeneous mixed boundary conditions. By using a double-level approximation method and some iterative techniques, we obtain the existence and time-space uniform boundedness of weak time periodic solutions for any m > 1. Moreover, we improve the regularity for m≤43 and show that the obtained periodic solutions are, in fact, strong periodic solutions.