On the Navier–Stokes equations on surfaces

  title={On the Navier–Stokes equations on surfaces},
  author={Jan Pruess and Gieri Simonett and Mathias Wilke},
  journal={arXiv: Analysis of PDEs},
We consider the motion of an incompressible viscous fluid that completely covers a smooth, compact and embedded hypersurface $\Sigma$ without boundary and flows along $\Sigma$. 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 $\Sigma$ and we show that each equilibrium on $\Sigma$ is stable. Moreover, it is shown that any solution starting close to an equilibrium exists… 

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