Semi-Discrete Optimal Transport Techniques for the Compressible Semi-Geostrophic Equations

In my research, I employ semi-discrete optimal transport methods to rigorously establish the uniqueness and existence of solutions for the three-dimensional compressible semi-geostrophic equations.

This mathematical framework strengthens the theoretical underpinnings of meteorological models but also enhances our understanding of how optimal transport techniques can be used for a multitude of partial differential equations.

Additionally, I utilize advanced numerical tools based on semi-discrete optimal transport to develop simulations of weather front formation and cyclones.

This dual approach of theoretical and numerical work provides a robust basis for improving weather forecasting techniques and offers significant insights into the behaviour of various atmospheric systems.