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VIDEO LIBRARY |
International conference Contemporary mathematics devoted to 80 anniversary of V. I. Arnold
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Beyond Arnold’s geodesic framework of an ideal hydrodynamics B. Khesin Department of Mathematics, University of Toronto |
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Abstract: In 1966 V.I. Arnold developed a group-theoretic approach to ideal hydrodynamics in which the Euler equation for an inviscid incompressible fluid is described as the geodesic flow equation for a right-invariant First of all, it was observed that problems of optimal mass transport are in a sense dual to the Euler hydrodynamics. By regarding volume-preserving diffeomorphisms as a subgroup of all diffeomorphisms, we describe The second generalization is an Arnold-like geodesic and Hamiltonian description for fluid flows with vortex sheets. It turns out that the corresponding dynamics is related to a certain groupoid of pairs of volume-preserving diffeomorphisms with common interface and equipped with a one-sided invariant metric. Language: English |