Section: Application Domains

Meteorology and Fluid models

In, [34] Brenier reviews in a unified framework the connection between optimal transport theory and classical convection theory for geophysical flows. Inspired by the numerical model proposed in [30] , the starting point is a generalization of the Darcy-Boussinesq equations, which is a degenerate version of the Navier-Stokes-Boussinesq (NSB) equations. In a unified framework, he relates different variants of the NSB equations (in particular what he calls the generalized hydrostatic-Boussinesq equations) to various models involving optimal transport and the related Monge-Ampère equation. This includes the 2D semi-geostrophic equations [61] [49] [48] [4] [67] and some fully nonlinear versions of the so-called high-field limit of the Vlasov-Poisson system [73] and of the Keller-Segel system for chemotaxis [63] [44] .