The semi-geostrophic system: weak-strong uniqueness under uniform convexity.

We prove a weak-strong uniqueness result for 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. We give several examples where our results apply, including some classical solutions on the 2-dimensional torus, and the 'stationary' solutions for 3DSG (for which the total wind velocity is zero but the pressure may be time-dependent). [ABSTRACT FROM AUTHOR]