Global solutions to a 3D chemotaxis-Stokes system with nonlinear cell diffusion and Robin signal boundary condition

In this paper, we investigate a 3D chemotaxis-Stokes system with general sensitivity, nonlinear cell diffusion and Robin signal boundary condition. After introducing a Lions-Magenes type transformation, we transform the Robin signal boundary condition into the usual homogeneous Neumann boundary value, and then use a two-step iterative method to establish the global existence of bounded weak solutions. Here, the key is to deal with the extra terms coming from the transformation. In the case of homogeneous Robin boundary value, we will adapt the method of Winkler (Calc. Var., 2015 [35]) to investigate the large time behavior and the eventual smoothness of the above weak solutions. (C) 2020 Elsevier Inc. All rights reserved.