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2020 Well-posedness of the hydrostatic Navier–Stokes equations
David Gérard-Varet, Nader Masmoudi, Vlad Vicol
Anal. PDE 13(5): 1417-1455 (2020). DOI: 10.2140/apde.2020.13.1417

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.

Citation

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David Gérard-Varet. Nader Masmoudi. Vlad Vicol. "Well-posedness of the hydrostatic Navier–Stokes equations." Anal. PDE 13 (5) 1417 - 1455, 2020. https://doi.org/10.2140/apde.2020.13.1417

Information

Received: 12 April 2018; Revised: 2 May 2019; Accepted: 11 June 2019; Published: 2020
First available in Project Euclid: 17 September 2020

zbMATH: 07271834
MathSciNet: MR4149066
Digital Object Identifier: 10.2140/apde.2020.13.1417

Subjects:
Primary: 35Q30
Secondary: 35Q35

Keywords: fluid mechanics , Navier–Stokes equations

Rights: Copyright © 2020 Mathematical Sciences Publishers

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