arXiv subjects

Roberto D'Onofrio

Publications and source records attributed to Roberto D'Onofrio.

3 recordsLinked to original sources

arXiv2024

Monge-Ampere Geometry and the Eady Problem

Chynoweth and Sewell proposed a mathematical model for an atmospheric front based on the singularities of the Legendre transformation between different pairs of dual variables. Drawing inspiration from their work, we formalize the idea of a Chynoweth-Sewell front and illuminate its geometrical meaning from the viewpoint of Monge-Ampere geometry. This extends our previous work on the semigeostrophic model to dynamically-forming singularities. We use the notion of a Chynoweth-Sewell front to characterize the classical Eady problem and its known solutions in geometrical terms.

math-ph↗

arXiv2023

A note on optimal transport and Monge-Ampère geometry

We identify a novel connection between a recently introduced pseudo-Riemannian framework for optimal mass transport and the geometry of Monge-Ampère equations. We show this correspondence by application to an example from geophysical fluid dynamics.

math-ph↗

arXiv2022

Solutions and Singularities of the Semigeostrophic Equations via the Geometry of Lagrangian Submanifolds

Using Monge-Ampère geometry, we study the singular structure of a class of nonlinear Monge-Ampère equations in three dimensions, arising in geophysical fluid dynamics. We extend seminal earlier work on Monge-Ampère geometry by examining the role of an induced metric on Lagrangian submanifolds of the cotangent bundle. In particular, we show that the signature of the metric serves as a classification of the Monge-Ampère equation, while singularities and elliptic-hyperbolic transitions are revealed by the degeneracies of the metric. The theory is illustrated by application to an example solution of the semigeostrophic equations.

math-ph↗