Optimal Transport and the Compressible Semi-Geostrophic Equations
Date:
The semi-geostrophic equations for a compressible fluid, first analyzed by Cullen and Maroofi [2003], provide a simplified model of the formation and evolution of atmospheric fronts. I will discuss the use of semi-discrete optimal transport theory to rigorously prove the existence of global-in-time weak solutions as the limit of spatially discrete approximations. This constructive proof of the existence of weak solutions directly extends the work of Bourne et al. [2022] from the incompressible to the compressible setting. I will also show some of the numerical results and discuss the challenges we faced in implementing this numerical method.
This is joint work with David Bourne, Charlie Egan and Beatrice Pelloni.