A fully nonlinear version of the incompressible Euler equations

The semigeostrophic system

Research output: Contribution to journalArticleResearchpeer-review

34 Citations (Scopus)

Abstract

The semigeostrophic equations are used in meteorology. They appear as a variant of the two-dimensional Euler incompressible equations in vorticity form, where the Poisson equation that relates the stream function and the vorticity field is just replaced by the fully nonlinear elliptic Monge-Ampère equation. This work gathers new results concerning the semigeostrophic equations: existence and stability of measure-valued solutions, existence and uniqueness of solutions under certain continuity conditions for the density, and convergence to the incompressible Euler equations.

Original languageEnglish
Pages (from-to)795-823
Number of pages29
JournalSIAM Journal on Mathematical Analysis
Volume38
Issue number3
DOIs
Publication statusPublished - 2006
Externally publishedYes

Keywords

  • Monge-Ampère equations
  • Optimal transportation
  • Semigeostrophic equations

Cite this

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A fully nonlinear version of the incompressible Euler equations : The semigeostrophic system. / Loeper, G.

In: SIAM Journal on Mathematical Analysis, Vol. 38, No. 3, 2006, p. 795-823.

Research output: Contribution to journalArticleResearchpeer-review

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T2 - The semigeostrophic system

AU - Loeper, G.

PY - 2006

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AB - The semigeostrophic equations are used in meteorology. They appear as a variant of the two-dimensional Euler incompressible equations in vorticity form, where the Poisson equation that relates the stream function and the vorticity field is just replaced by the fully nonlinear elliptic Monge-Ampère equation. This work gathers new results concerning the semigeostrophic equations: existence and stability of measure-valued solutions, existence and uniqueness of solutions under certain continuity conditions for the density, and convergence to the incompressible Euler equations.

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KW - Optimal transportation

KW - Semigeostrophic equations

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JF - SIAM Journal on Mathematical Analysis

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