Well-posedness of the hydrostatic Navier-Stokes equations
Analysis of PDEs
2018-04-13 v1
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.
Cite
@article{arxiv.1804.04489,
title = {Well-posedness of the hydrostatic Navier-Stokes equations},
author = {David Gerard-Varet and Nader Masmoudi and Vlad Vicol},
journal= {arXiv preprint arXiv:1804.04489},
year = {2018}
}