Boris Khesin, "Beyond Arnold's geodesic framework of an ideal hydrodynamics"
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Europe/Rome
Ex-ISEF/Building-Main Lecture Hall (GSSI)
Ex-ISEF/Building-Main Lecture Hall
GSSI
20
Description
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.
