Lecture notes on variational models for incompressible Euler equations

TL;DR

This paper summarizes recent developments in Brenier's variational models for the incompressible Euler equations, highlighting their theoretical foundations and applications in optimal transportation.

Contribution

It provides an overview of recent results on variational models for the Euler equations, connecting optimal transportation theory with fluid dynamics.

Findings

Brenier's variational models offer a new perspective on incompressible flows.

Recent results demonstrate the effectiveness of these models in describing fluid behavior.

The notes highlight the connection between optimal transportation and Euler equations.

Abstract

These notes briefly summarize the lectures for the Summer School "Optimal transportation: Theory and applications" held by the second author in Grenoble during the week of June 22-26, 2009. Their goal is to describe some recent results on Brenier's variational models for incompressible Euler equation.