Well-posedness of the hydrostatic Navier-Stokes equations

David Gérard-Varet, Nader Masmoudi, Vlad Vicol

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)1417-1455
Number of pages39
JournalAnalysis and PDE
Volume13
Issue number5
DOIs
StatePublished - 2020

Keywords

  • Fluid mechanics
  • Navier-Stokes equations

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Applied Mathematics

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