Singularities in geophysical fluid dynamics through Monge-Ampère geometry

Time：2023-04-28 Fri 17:00-18:30

Venue：ZOOM: 815 4690 4797（PW: BIMSA）

Organizer：Nicolai Reshetikhin, Andrey Tsiganov, Ivan Sechin

Speaker：Roberto D'Onofrio Università Bicocca and University of Surrey

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

DATEApril 28, 2023

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