Global bounded solution of a 3D chemotaxis-Stokes system with slow $ p $-Laplacian diffusion and logistic source

Abstract

<abstract><p>In this paper, the chemotaxis-Stokes system with slow $ p $-Laplacian diffusion and logistic source as follows</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{equation*} \left\{ \begin{aligned} &amp;n_t+u\cdot\nabla n = \nabla\cdot(|\nabla n|^{p-2}\nabla n)-\nabla\cdot(n\nabla c)+\mu n(1-n), &amp;x\in\Omega, t&gt;0, \\ &amp;c_t+u\cdot\nabla c = \Delta c-cn, &amp; x\in\Omega, t&gt;0, \\ &amp;u_t+\nabla P = \Delta u+n\nabla\Phi, &amp; x\in\Omega, t&gt;0, \\ &amp;\nabla\cdot u = 0, &amp;\; x\in\Omega, t&gt;0\; \end{aligned} \right. \end{equation*} $\end{document} </tex-math></disp-formula></p> <p>was considered in a bounded domain $ \Omega\subset\mathbb{R}^3 $ with smooth boundary under homogeneous Neumann-Neumann-Dirichlet boundary conditions. Subject to the effect of logistic source, we proved the system exists a global bounded weak solution for any $ p &gt; 2 $.</p></abstract>