Geometry of generalized fluid flows

Anton Izosimov, Boris Khesin

Research output: Contribution to journalArticlepeer-review


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 L2 -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.

Original languageEnglish (US)
Article number3
JournalCalculus of Variations and Partial Differential Equations
Issue number1
StatePublished - Jan 2024

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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