A fully nonlinear version of the incompressible Euler equations: The semigeostrophic system

G. Loeper

Research output: Contribution to journalArticleResearchpeer-review

42 Citations (Scopus)


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
Issue number3
Publication statusPublished - 2006
Externally publishedYes


  • Monge-Ampère equations
  • Optimal transportation
  • Semigeostrophic equations

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