Boundedness of weak solutions in a 3D chemotaxis-Stokes system with nonlinear doubly degenerate diffusion

In this paper, the following incompressible chemotaxis-Stokes system with nonlinear doubly degenerate diffusion is considered in a smooth bounded domain Omega subset of R-3: {n(t) + u. del n = del . (vertical bar del(m)(n)vertical bar(p-2)del(m)(n)) -del . (n del c), x is an element of Omega, t > 0, c(t) + u . del c = Delta c - nc, x is an element of Omega, t > 0, u(t) = Delta u + del P + n del phi, x is an element of Omega, t > 0, del . u = 0, x is an element of Omega, t > 0, where the potential function phi is an element of W-2,W-infinity(Omega) is given. For homogeneous boundary conditions of Neumann type for n and c, and of Dirichlet type for u, it is proved that global bounded weak solutions exist for suitable regular initial data whenever 8mp - 8m + 3p > 15, p >= 2 and m >= 1. (C) 2021 Elsevier Inc. All rights reserved.