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

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

Fingerprint

Cauchy's integral theorem
Primitive Equations
Incompressible Euler Equations
Space of Analytic Functions
Hydrostatics
Local Existence
Euler equations
Analyticity
Euler Equations
Analytic Solution
Well-posedness
Bounded Domain
Cauchy Problem
Existence and Uniqueness
Radius
Decay

Keywords

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

ASJC Scopus subject areas

  • Analysis

Cite this

Local existence and uniqueness for the hydrostatic Euler equations on a bounded domain. / Kukavica, Igor; Temam, Roger; Vicol, Vlad; Ziane, Mohammed.

In: Journal of Differential Equations, Vol. 250, No. 3, 01.02.2011, p. 1719-1746.

Research output: Contribution to journalArticle

Kukavica, Igor ; Temam, Roger ; Vicol, Vlad ; Ziane, Mohammed. / Local existence and uniqueness for the hydrostatic Euler equations on a bounded domain. In: Journal of Differential Equations. 2011 ; Vol. 250, No. 3. pp. 1719-1746.
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