Local existence of smooth solutions for the semigeostrophic equations on curved domains

2022/06/13 by Silini, Lauro · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2206.06191

Abstract

We prove local-in-time existence of smooth solutions to the semigeostrophic equations in the general setting of smooth, bounded and simply connected domains of ℝ² endowed with an arbitrary conformally flat metric and non-vanishing Coriolis term. We present a construction taking place in Eulerian coordinates, avoiding the classical reformulation in dual variables, used in the flat case with constant Coriolis force, but lacking in this general framework.

Cited by

• Semi-discrete optimal transport techniques for the compressible semi-geostrophic equations

Related

• Local-in-time Physical Solutions of the Incompressible Semi-Geostrophic Equations in Eulerian Coordinates
• Smooth Solutions of the Surface Semi-Geostrophic Equations
• Existence of Eulerian solutions to the semigeostrophic equations in physical space: the 2-dimensional periodic case
• A global existence result for the semigeostrophic equations in three dimensional convex domains
• Long time existence of smooth solutions to semigeostrophic equations on a torus