Global existence in a three-dimensional chemotaxis-Stokes system with ρ-Laplacian diffusion and singular sensitivity

This paper considers the following chemotaxis-Stokes system {n(t)+u & sdot;del(n)=del & sdot;(|del n|(p-2)del(n))-chi del & sdot;((n)/(c)del c)+n(r-mu n(delta)), c(t)+u & sdot;del c=Delta c-nc, u(t)=Delta u+del P+n del Phi in a smooth bounded domain Omega subset of R-3 with no-flux/no-flux/Dirichlet boundary conditions. It is shown that there exists a global weak solution when p >= 2 and delta>(3)/(2), which removes the restriction p> min {(6 delta+1)/(2(2 delta-1)), (2 delta(delta+2))/((2 delta+3)(delta-1)) and improves the result of the paper (Han and Liu, 2023).