Well-posedness and convergence of entropic approximation of semi-geostrophic equations

TL;DR

This paper proves the existence, uniqueness, and convergence of solutions for an entropic approximation of semi-geostrophic equations, linking numerical discretizations to weak solutions as the entropic parameter approaches zero.

Contribution

It introduces an entropic formulation for semi-geostrophic equations and demonstrates convergence to classical solutions, including practical numerical discretizations.

Findings

Existence and uniqueness of solutions for the entropic semi-geostrophic equations

Convergence of entropic solutions to weak solutions as the entropic parameter vanishes

Validation of discretizations that are computationally feasible

Abstract

We prove existence and uniqueness of solutions for an entropic version of the semi-geostrophic equations. We also establish convergence to a weak solution of the semi-geostrophic equations as the entropic parameter vanishes. Convergence is also proved for discretizations that can be computed numerically in practice as shown recently in [6].