From Euler to the semi-geostrophic system: convergence under uniform convexity

Abstract

We prove that if the initial data is well prepared, then certain solutions to the Euler system converge to a solution of the Semi-Geostrophic system with constant Coriolis force. The main assumptions on the strong solution are the boundedness of the velocity field as well as the uniform convexity of the Legendre-Fenchel transform of the modified pressure.