Symplectic structures and dynamics on vortex membranes

zbMath1258.35162arXiv1201.5914MaRDI QIDQ4902664

Boris A. Khesin

Publication date: 17 January 2013

Full work available at URL: https://arxiv.org/abs/1201.5914

zbMATH Keywords

mean curvature flowEuler equationsymplectic structurevortex filament equationvortex sheetlocalized induction approximationvortex membrane

Mathematics Subject Classification ID

Variational aspects of group actions in infinite-dimensional spaces (58E40) Euler equations (35Q31)

Related Items

Global transversal stability of Euclidean planes under skew mean curvature flow evolutions ⋮ Dynamics of symplectic fluids and point vortices ⋮ A novel formulation of point vortex dynamics on the sphere: geometrical and numerical aspects ⋮ Gauss map of the skew mean curvature flow ⋮ Coadjoint orbits of vortex sheets in ideal fluids ⋮ Pointed vortex loops in ideal 2D fluids ⋮ Geometric hydrodynamics in open problems ⋮ Local well-posedness of the skew mean curvature flow for small data in \(d \geqq 2\) dimensions ⋮ Skew mean curvature flow ⋮ Double extensions of Lie algebras of Kac-Moody type and applications to some Hamiltonian systems ⋮ Reconstruction phases in the planar three- and four-vortex problems ⋮ On the vortex filament conjecture for Euler flows ⋮ Vortex motion of the Euler and lake equations ⋮ Vortex sheets and diffeomorphism groupoids ⋮ Local existence and uniqueness of skew mean curvature flow ⋮ Global and local theory of skew mean curvature flows ⋮ Higher-dimensional Euler fluids and Hasimoto transform: counterexamples and generalizations ⋮ Local well-posedness of skew mean curvature flow for small data in \(d\ge 4\) dimensions ⋮ Riemannian geometry of the contactomorphism group

This page was built for publication: Symplectic structures and dynamics on vortex membranes