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Integrability of Po...
Integrability of Point-Vortex Dynamics via Symplectic Reduction: A Survey
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- Modin, Klas, 1979 (author)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences
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- Viviani, Milo, 1991 (author)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences
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(creator_code:org_t)
- 2020-10-15
- 2021
- English.
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In: Arnold Mathematical Journal. - : Springer Science and Business Media LLC. - 2199-6792 .- 2199-6806. ; 7:3, s. 357-385
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Abstract
Subject headings
Close
- Point-vortex dynamics describe idealized, non-smooth solutions to the incompressible Euler equations on two-dimensional manifolds. Integrability results for few point-vortices on various domains is a vivid topic, with many results and techniques scattered in the literature. Here, we give a unified framework for proving integrability results for N= 2 , 3, or 4 point-vortices (and also more general Hamiltonian systems), based on symplectic reduction theory. The approach works on any two-dimensional manifold with a symmetry group; we illustrate it on the sphere, the plane, the hyperbolic plane, and the flat torus. A systematic study of integrability is prompted by advances in two-dimensional turbulence, bridging the long-time behaviour of 2D Euler equations with questions of point-vortex integrability. A gallery of solutions is given in the appendix.
Subject headings
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
- NATURVETENSKAP -- Matematik -- Geometri (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Geometry (hsv//eng)
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Keyword
- Integrable systems
- Point-vortex dynamics
- Symplectic reduction
- Euler equations
- Euler equations
- Integrable systems
- Point-vortex dynamics
- Symplectic reduction
Publication and Content Type
- art (subject category)
- ref (subject category)
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