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

Igor Kukavica; Roger Temam; Vlad C. Vicol; Mohammed Ziane

doi:10.1016/j.jde.2010.07.032

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

Igor Kukavica, Roger Temam, Vlad C. Vicol, Mohammed Ziane

Mathematics

Research output: Contribution to journal › Article › peer-review

48 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 language	English (US)
Pages (from-to)	1719-1746
Number of pages	28
Journal	Journal of Differential Equations
Volume	250
Issue number	3
DOIs	https://doi.org/10.1016/j.jde.2010.07.032
State	Published - 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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10.1016/j.jde.2010.07.032

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title = "Local existence and uniqueness for the hydrostatic Euler equations on a bounded domain",

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.",

keywords = "Analyticity, Bounded domain, Hydrostatic Euler equations, Hydrostatic approximation, Non-viscous primitive equations, Well-posedness",

author = "Igor Kukavica and Roger Temam and Vicol, {Vlad C.} and Mohammed Ziane",

note = "Funding Information: The work of I.K. and V.V. was supported in part by the NSF grant DMS-1009769, the work of R.T. was partially supported by the National Science Foundation under the grant NSF-DMS-0906440 and by the Research Fund of Indiana University, while M.Z. was supported in part by the NSF grant DMS-0505974.",

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T1 - Local existence and uniqueness for the hydrostatic Euler equations on a bounded domain

AU - Kukavica, Igor

AU - Temam, Roger

AU - Vicol, Vlad C.

AU - Ziane, Mohammed

N1 - Funding Information: The work of I.K. and V.V. was supported in part by the NSF grant DMS-1009769, the work of R.T. was partially supported by the National Science Foundation under the grant NSF-DMS-0906440 and by the Research Fund of Indiana University, while M.Z. was supported in part by the NSF grant DMS-0505974.

PY - 2011/2/1

Y1 - 2011/2/1

N2 - 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.

AB - 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.

KW - Analyticity

KW - Bounded domain

KW - Hydrostatic Euler equations

KW - Hydrostatic approximation

KW - Non-viscous primitive equations

KW - Well-posedness

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DO - 10.1016/j.jde.2010.07.032

M3 - Article

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SN - 0022-0396

VL - 250

SP - 1719

EP - 1746

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 3

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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