Solutions of the semigeostrophic equation on a rotating sphere

Mathphys Analysis Seminar

Hoskins' semigeostrophic equation is one of the most effective meteorological model that represents the formation of transported interfaces (frontogenesis) over the earth. We will present its surprising connection with the theory of optimal transportation when studied in the periodic and flat case, and highlight the major difficulties to extend this argument in the curved setting. We prove local-in-time existence of smooth solutions in subdomains of a rotating sphere taking advantage of an alternative approach based on peculiar cancellation properties intrinsic in the equation's structure.