Saturation of the signal on the boundary: global weak solvability in a chemotaxis-Stokes system with porous-media type cell diffusion (Q2074477)

In this paper, the authors study a chemotaxis-Stokes system with porous medium diffusion \(\Delta n^m\) in a bounded domain of \(\mathbb R^N\) with \(N=2, 3\). Different from the homogeneous boundary value problem, the authors consider the signal to attain a prescribed saturation value on the boundary. Using the energy method and some compactness discussions, they prove the existence of global bounded weak solutions for the case \(m>\frac{3N-2}{2N}\).