Hamiltonian dynamics behind compressible fluids


Khesin, B. (2023). Hamiltonian dynamics behind compressible fluids. Perimeter Institute. https://pirsa.org/23020046


Khesin, Boris. Hamiltonian dynamics behind compressible fluids. Perimeter Institute, Feb. 03, 2023, https://pirsa.org/23020046


          @misc{ pirsa_23020046,
            doi = {10.48660/23020046},
            url = {https://pirsa.org/23020046},
            author = {Khesin, Boris},
            keywords = {Mathematical physics},
            language = {en},
            title = {Hamiltonian dynamics behind compressible fluids},
            publisher = {Perimeter Institute},
            year = {2023},
            month = {feb},
            note = {PIRSA:23020046 see, \url{https://pirsa.org}}

Boris Khesin University of Toronto


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.

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