On the H S Theory of Hydrostatic Euler Equations

Nader Masmoudi, Tak Kwong Wong

Research output: Contribution to journalArticle

Abstract

In this paper we study the two-dimensional hydrostatic Euler equations in a periodic channel. We prove the local existence and uniqueness of H S solutions under the local Rayleigh condition. This extends Brenier's (Nonlinearity 12(3):495-512, 1999) existence result by removing an artificial condition and proving uniqueness. In addition, we prove weak-strong uniqueness, mathematical justification of the formal derivation and stability of the hydrostatic Euler equations. These results are based on weighted H S a priori estimates, which come from a new type of nonlinear cancellation between velocity and vorticity.

Original languageEnglish (US)
Pages (from-to)231-271
Number of pages41
JournalArchive for Rational Mechanics and Analysis
Volume204
Issue number1
DOIs
StatePublished - Apr 2012

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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