Abstract

The semigeostrophic equations are a mathematical model representing atmospheric motion on a subcontinental scale. Their remarkable mathematical features enable the equations to model singular behaviours like weather fronts. This talk presents a new approach to classifying these singular structures using the geometry of Monge-Ampère equations. In the geometrical view, solutions are understood as Lagrangian submanifolds of a suitably defined phase space equipped with a pseudo-Riemannian metric. We show the interplay between solution singularities, elliptic-hyperbolic transitions of the Monge-Ampère operator, and the degeneracies of the metric on a few examples