| Abstract: |
| In this talk, we focus on the Keller-Segel-(Navier-)Stokes system with tensor-valued sensitivity and logistic source in a bounded domain $\Omega\subset\mathbb{R}^N$ subject to no-flux/Dirichlet/Dirichlet boundary conditions for cells/signal/fluid, respectively. We will show that when $N=2$, the Keller-Segel-Navier-Stokes system admits a global bounded classical solution for any regular initial data. When $N=3$ similar conclusion holds for the Keller-Segel-Stokes system provided that the logistic damping is strong enough in some sense. We will also give some stabilization analysis under some additional assumptions. This is a joint work with Dr Yifei Sun and Dr Yu Tian. |
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