Global bounded weak solutions to a 3D chemotaxis-Stokes system with slow <inline-formula><tex-math id="M1">$ p- $</tex-math></inline-formula>Laplacian diffusion and rotation under Dirichlet signal boundary condition

In this paper, we consider the following chemotaxis-Stokes system with $ p- $Laplacian diffusion and rotation$ \begin{equation*} \left\{ \begin{aligned} & n_{t}+u\cdot \nabla n = \nabla\cdot(|\nabla n|^{p-2}\nabla n)-\nabla\cdot (nS(x,n,c)\nabla c),&& x\in \Omega ,t> 0,\\ & c_{t}+u\cdot \nabla c = \Delta c-nc,&& x\in \Omega ,t> 0,\\ & u_{t}+\nabla P = \Delta u+n\nabla \phi,&& x\in \Omega ,t> 0,\\ &\nabla \cdot u = 0, && x\in \Omega ,t> 0 \end{aligned} \right. \end{equation*} $in a smoothly bounded domain $ \Omega\subset\mathbb{R}^3 $ with inhomogeneous Dirichlet boundary condition. We obtain the boundedness of the global weak solutions to the initial-boundary value problem of the 3D chemotaxis-Stokes system with $ p- $Laplacian diffusion if $ p>\frac{19+\sqrt{201}}{16} $.