Talk page

Title:
Hamiltonian geometry behind compressible fluids

Speaker:
Boris Khesin

Abstract:
We describe a geometric framework to study Newton's equations on infinite-dimensional configuration spaces of diffeomorphisms and smooth probability densities. It turns out that several important PDEs of hydrodynamical origin can be described in this framework in a natural way. In particular, the so-called Madelung transform between the Schrödinger-type equations on wave functions and Newton's equations on densities turns out to be a Kähler map between the corresponding phase spaces, equipped with the Fubini-Study and Fisher-Rao information metrics. This is a joint work with G.Misiolek and K.Modin.

Link:
https://www.ias.edu/video/hamiltonian-geometry-behind-compressible-fluids