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BIMSA Integrable Systems Seminar
Singularities in geophysical fluid dynamics through Monge-Ampère geometry
Singularities in geophysical fluid dynamics through Monge-Ampère geometry
演讲者
Roberto D'Onofrio
时间
2023年04月28日 17:00 至 18:30
地点
Online
摘要
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