Section: Application Domains

Meteorology and Fluid models

In, [22] 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 [17] , 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 [51] [38] [37] [4] [57] and some fully nonlinear versions of the so-called high-field limit of the Vlasov-Poisson system [65] and of the Keller-Segel system for chemotaxis [53] [33] .