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A fully non-linear version of the Euler incompressible equations: the semi-geostrophic system

G. Loeper
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Abstract

This work gathers new results concerning the semi-geostrophic equations: existence and stability of measure valued solutions, existence and uniqueness of solutions under certain continuity conditions for the density, convergence to the incompressible Euler equations. Meanwhile, a general technique to prove uniqueness of sufficiently smooth solutions to non-linearly coupled system is introduced, using optimal transportation.

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G. Loeper. 2005-04-07. A fully non-linear version of the Euler incompressible equations: the semi-geostrophic system. https://arxiv.org/abs/math/0504138

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