Existence of Eulerian Solutions to the Semigeostrophic Equations in Physical Space: The 2-Dimensional Periodic Case

Luigi Ambrosio, Maria Colombo, Guido de Philippis, Alessio Figalli

Research output: Contribution to journalArticle


In this article we use new regularity and stability estimates for Alexandrov solutions to Monge-Ampère equations, recently established by De Philippis and Figalli [14], to provide global in time existence of distributional solutions to the semigeostrophic equations on the 2-dimensional torus, under very mild assumptions on the initial data. A link with Lagrangian solutions is also discussed.

Original languageEnglish (US)
Pages (from-to)2209-2227
Number of pages19
JournalCommunications in Partial Differential Equations
Issue number12
StatePublished - Jan 1 2012



  • Lagrangian flow
  • Optimal transporation
  • Semigeostrophic equations

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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