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

Abstract

This paper considers the following chemotaxis-Stokes system $\left(\begin{array}{cc}& n_t+u\cdot \nabla n=\nabla \cdot \left({\left(\nabla n\right)}^{p-2}\nabla n\right)-\chi \nabla \cdot (\frac{n}{c}\nabla c)+n\left(r-\mu n^{\delta }\right),\\ & c_t+u\cdot \nabla c=\Delta c-nc,\\ & u_t=\Delta u+\nabla P+n\nabla \Phi \end{array}\right)$in a smooth bounded domain $\Omega \subset R^3$ with no-flux/no-flux/Dirichlet boundary conditions. It is shown that there exists a global weak solution when $p\ge 2$ and $\delta >\frac{3}{2}$, which removes the restriction $p>\text{min}\left(\frac{6\delta +1}{2\left(2\delta -1\right)},\frac{2\delta \left(\delta +2\right)}{\left(2\delta +3\right)\left(\delta -1\right)}\right)$ and improves the result of the paper (Han and Liu, 2023).