In this paper we use the new regularity and stability estimates for Alexandrov solutions to Monge-Ampere equations estabilished by G.De Philippis and A.Figalli to provide a global in time existence of distributional solutions to a semigeostrophic equation on the 2-dimensional torus, under very mild assumptions on the initial data. A link with Lagrangian solutions is also discussed.

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

De Philippis, Guido;
2012-01-01

Abstract

In this paper we use the new regularity and stability estimates for Alexandrov solutions to Monge-Ampere equations estabilished by G.De Philippis and A.Figalli to provide a global in time existence of distributional solutions to a semigeostrophic equation on the 2-dimensional torus, under very mild assumptions on the initial data. A link with Lagrangian solutions is also discussed.
2012
37
12
2209
2227
https://arxiv.org/abs/1111.7202
Ambrosio, L; Colombo, M; De Philippis, Guido; Figalli, A.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/15849
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