| Abstract: |
| In this talk, we are concerned with the following chemotaxis-Stokes system with p-Laplacian diffusion and rotation
$\begin{equation*}
\left\{
\begin{split}
&n_{t}+u\cdot \nabla n=\nabla\cdot(|\nabla n|^{p-2}\nabla n)-\nabla\cdot (nS(x,n,c)\nabla c),&&x\in \Omega ,t> 0,\
& c_{t}+u\cdot \nabla c=\Delta c-nc,&&x\in \Omega ,t> 0,\
& u_{t}+\nabla P=\Delta u+n\nabla \phi,&&x\in \Omega ,t> 0,\
&\nabla \cdot u=0, &&x\in \Omega ,t> 0
\end{split}
\right.
\end{equation*}$
in a smooth bounded domain $\Omega\in\mathbb{R}^3$. We show the boundedness of the weak solutions to the 3D chemotaxis-Stokes system with p-Laplacian diffusion under no-flux boundary conditions/Dirichlet signal boundary condition. |
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