论文标题
在表面上的Navier-Stokes方程式上
On the Navier-Stokes equations on surfaces
论文作者
论文摘要
我们考虑了不可压缩的粘性流体的运动，该运动完全涵盖了平滑，紧凑和嵌入式的超出表面$σ$，而无需边界并沿$σ$流动。 $ l_p $ - $ l_q $ -maximal的规律性的框架中建立了当地的适合度。我们将一组平衡表征为$σ$上所有杀死向量场的集合，我们表明$σ$上的每个平衡都是稳定的。此外，显示出任何启动接近平衡的溶液均在全球存在，并以指数速率收敛至（可能不同）的平衡，因为时间趋于无穷大。
We consider the motion of an incompressible viscous fluid that completely covers a smooth, compact and embedded hypersurface $Σ$ without boundary and flows along $Σ$. Local-in-time well-posedness is established in the framework of $L_p$-$L_q$-maximal regularity. We characterize the set of equilibria as the set of all Killing vector fields on $Σ$ and we show that each equilibrium on $Σ$ is stable. Moreover, it is shown that any solution starting close to an equilibrium exists globally and converges at an exponential rate to a (possibly different) equilibrium as time tends to infinity.
