Semi-geostrophic System with Variable Coriolis parameter

Abstract

We prove short time existence and uniqueness of smooth solutions ( in $C^{k+2,\alpha }$ with $k\ge 2$) to the 2-D semi-geostrophic system and semi-geostrophic shallow water system with variable Coriolis parameter $f$ and periodic boundary conditions, under the natural convexity condition on the initial data. The dual space used in analysis of the semi-geostrophic system with constant $f$ does not exist for the variable Coriolis parameter case, and we develop a time-stepping procedure to overcome this difficulty.

49 pages

Cited by in corpus (1)

• Semi-discrete optimal transport methods for the semi-geostrophic equations