Global weak solutions in a three-dimensional Keller-Segel-Navier-Stokes system with nonlinear diffusion

摘要

The coupled quasilinear Keller-Segel-Navier-Stokes system is considered underNeumann boundary conditions for $n$ and $c$ and no-slip boundary conditions for$u$ in three-dimensional bounded domains $\Omega\subseteq \mathbb{R}^3$ withsmooth boundary, where $m>0,\kappa\in \mathbb{R}$ are given constants, $\phi\inW^{1,\infty}(\Omega)$. If $ m> 2$, then for all reasonably regular initialdata, a corresponding initial-boundary value problem for $(KSNF)$ possesses aglobally defined weak solution.