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arXiv · 1804.04489

Well-posedness of the hydrostatic Navier-Stokes equations

David Gerard-Varet·Nader Masmoudi·Vlad Vicol
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Abstract

We address the local well-posedness of the hydrostatic Navier-Stokes equations. These equations, sometimes called reduced Navier-Stokes/Prandtl, appear as a formal limit of the Navier-Stokes system in thin domains, under certain constraints on the aspect ratio and the Reynolds number. It is known that without any structural assumption on the initial data, real-analyticity is both necessary and sufficient for the local well-posedness of the system. In this paper we prove that for convex initial data, local well-posedness holds under simple Gevrey regularity.

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David Gerard-Varet, Nader Masmoudi, Vlad Vicol. 2018-04-12. Well-posedness of the hydrostatic Navier-Stokes equations. https://arxiv.org/abs/1804.04489

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