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- Title
Geometry of generalized fluid flows.
- Authors
Izosimov, Anton; Khesin, Boris
- Abstract
The Euler equation of an ideal (i.e. inviscid incompressible) fluid can be regarded, following V. Arnold, as the geodesic flow of the right-invariant L 2 -metric on the group of volume-preserving diffeomorphisms of the flow domain. In this paper we describe the common origin and symmetry of generalized flows, multiphase fluids (homogenized vortex sheets), and conventional vortex sheets: they all correspond to geodesics on certain groupoids of multiphase diffeomorphisms. Furthermore, we prove that all these problems are Hamiltonian with respect to a Poisson structure on a dual Lie algebroid, generalizing the Hamiltonian property of the Euler equation on a Lie algebra dual.
- Subjects
FLUID flow; GEODESIC flows; GEOMETRY; LIE algebras; EULER equations; DIFFEOMORPHISMS; YANG-Baxter equation; INVISCID flow
- Publication
Calculus of Variations & Partial Differential Equations, 2024, Vol 63, Issue 1, p1
- ISSN
0944-2669
- Publication type
Article
- DOI
10.1007/s00526-023-02612-5