Geometric Hydrodynamics via Madelung Transform
| Autor: | Khesin, Boris, Misiolek, Gerard, Modin, Klas |
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| Rok vydání: | 2017 |
| Předmět: | |
| Zdroj: | PNAS, 115(24):6165-6170, 2018 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1073/pnas.1719346115 |
| Popis: | 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 PDEs of hydrodynamical origin can be described in this framework in a natural way. In particular, the Madelung transform between the Schr\"odinger equation and Newton's equations is a symplectomorphism of the corresponding phase spaces. Furthermore, the Madelung transform turns out to be a K\"ahler map when the space of densities is equipped with the Fisher-Rao information metric. We describe several dynamical applications of these results. Comment: 17 pages, 2 figures |
| Databáze: | arXiv |
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