Abstract
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 language | English (US) |
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Pages (from-to) | 2209-2227 |
Number of pages | 19 |
Journal | Communications in Partial Differential Equations |
Volume | 37 |
Issue number | 12 |
DOIs | |
State | Published - Jan 2012 |
Keywords
- Lagrangian flow
- Optimal transporation
- Semigeostrophic equations
ASJC Scopus subject areas
- Analysis
- Applied Mathematics