Vortex rings in a cylinder and rearrangements

DOI10.1016/0022-0396(87)90155-0zbMath0648.35029OpenAlexW2045520223MaRDI QIDQ1105116

Geoffrey R. Burton

Publication date: 1987

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-0396(87)90155-0

zbMATH Keywords

cylindrical coordinatesrearrangementvariational problemsdistribution functionSteiner symmetrizationvortex rings

Mathematics Subject Classification ID

Vortex flows for incompressible inviscid fluids (76B47) Variational methods for second-order elliptic equations (35J20)

Related Items

Clustered travelling vortex rings to the axisymmetric three-dimensional incompressible Euler flows ⋮ Multiscale Steady Vortex Patches for 2D Incompressible Euler Equations ⋮ Asymptotic behaviour of global vortex rings ⋮ Rearrangements of functions on unbounded domains ⋮ Desingularization of vortex rings in 3 dimensional Euler flows ⋮ Regularization of point vortices pairs for the Euler equation in dimension two ⋮ Steady symmetric vortex pairs and rearrangements ⋮ Planar vortex patch problem in incompressible steady flow ⋮ Steady vortex patches with opposite rotation directions in a planar ideal fluid ⋮ Existence of steady symmetric vortex patch in a disk ⋮ Desingularization of vortices for the Euler equation ⋮ Desingularization of vortex rings and shallow water vortices by a semilinear elliptic problem ⋮ Steady vortex patch with polygonal symmetry for the planar Euler equations in a disc ⋮ Nonlinear stability of planar vortex patches in an ideal fluid ⋮ Steady vortex rings in a uniform flow and rearrangements of a function ⋮ Regularization of planar vortices for the incompressible flow ⋮ Local uniqueness for vortex patch problem in incompressible planar steady flow

Cites Work

• Unnamed Item
• Unnamed Item
• Rearrangements of functions, maximization of convex functionals, and vortex rings
• The uniqueness of Hill's spherical vortex
• Rearrangement inequalities and duality theory for a semilinear elliptic variational problem
• A global theory of steady vortex rings in an ideal fluid