Geometric hydrodynamics and infinite-dimensional Newton's equations

Autor:	Khesin, Boris, Misiolek, Gerard, Modin, Klas
Rok vydání:	2020
Předmět:	Mathematics - Symplectic Geometry Mathematical Physics Mathematics - Differential Geometry 37K65 76M60
Zdroj:	Bull. Amer. Math. Soc. 58, 377-442 (2021)
Druh dokumentu:	Working Paper
DOI:	10.1090/bull/1728
Popis:	We revisit the geodesic approach to ideal hydrodynamics and present a related geometric framework for Newton's equations on groups of diffeomorphisms and spaces of probability densities. The latter setting is sufficiently general to include equations of compressible and incompressible fluid dynamics, magnetohydrodynamics, shallow water systems and equations of relativistic fluids. We illustrate this with a survey of selected examples, as well as with new results, using the tools of infinite-dimensional information geometry, optimal transport, the Madelung transform, and the formalism of symplectic and Poisson reduction. Comment: 62 pages. Revised version, accepted in Bull. AMS
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2001.01143 Zobrazit plný text záznamu View this record from Arxiv