Local existence and uniqueness for the hydrostatic Euler equations on a bounded domain

Igor Kukavica, Roger Temam, Vlad Vicol, Mohammed Ziane

Research output: Contribution to journalArticle

28 Scopus citations

Abstract

We address the question of well-posedness in spaces of analytic functions for the Cauchy problem for the hydrostatic incompressible Euler equations (inviscid primitive equations) on domains with boundary. By a suitable extension of the Cauchy-Kowalewski theorem we construct a locally in time, unique, real-analytic solution and give an explicit rate of decay of the radius of real-analyticity.

Original languageEnglish (US)
Pages (from-to)1719-1746
Number of pages28
JournalJournal of Differential Equations
Volume250
Issue number3
DOIs
StatePublished - Feb 1 2011

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Keywords

  • Analyticity
  • Bounded domain
  • Hydrostatic Euler equations
  • Hydrostatic approximation
  • Non-viscous primitive equations
  • Well-posedness

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