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• W2765749019 abstract "We introduce 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 partial differential equations of hydrodynamical origin can be described in this framework in a natural way. In particular, the Madelung transform between the Schrödinger equation and Newton's equations is a symplectomorphism of the corresponding phase spaces. Furthermore, the Madelung transform turns out to be a Kähler map when the space of densities is equipped with the Fisher-Rao information metric. We describe several dynamical applications of these results." @default.
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• W2765749019 date "2018-05-29" @default.
• W2765749019 modified "2023-09-28" @default.
• W2765749019 title "Geometric hydrodynamics via Madelung transform" @default.
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• W2765749019 doi "https://doi.org/10.1073/pnas.1719346115" @default.
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