Boundedness and global solvability to a chemotaxis model with nonlinear diffusion

In this paper, we study a chemotaxis model with nonlinear diffusion Δum (m>1). We consider this problem in a bounded domain Ω⊂R3 with zero-flux boundary condition, and it is shown that for any large initial datum, for any m>1, the problem admits a global weak solution, which is uniformly bounded.