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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–Ampere 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.

A Fully Nonlinear Version of the Incompressible Euler Equations: The Semigeostrophic System