250120 VO Optimal transport methods for hamiltonian PDEs (2016S)

In the last 25 years, Optimal transport theory, which lies between Calculus of Variations, Probability and Geometry, has been used many times to address non-linear elliptic PDEs, such as
the real Monge-Ampere equation, or parabolic equations such as the heat equation and many nonlinear generalizations. Its link with conservative, hamiltonian and hyperbolic PDEs is much less documented.

The aim of this course is to cover two important examples: namely the Euler equations of incompressible fluids, which goes back to the 18th
century (few years before Monge introduced the first optimal transport problem) and the Born-Infeld equations of Electromagnetism which goes back to 1934 and has been revisited in the 90s by High Energy Physicists.