Vortex Rings: Existence and Asymptotic Estimates
- 1 November 1981
- journal article
- Published by JSTOR in Transactions of the American Mathematical Society
- Vol. 268 (1) , 1-37
- https://doi.org/10.2307/1998335
Abstract
The existence of a family of steady vortex rings is established by a variational principle. Further, the asymptotic behavior of the solutions is obtained for limiting values of an appropriate parameter $\lambda$; as $\lambda \to \infty$ the vortex ring tends to a torus whose cross-section is an infinitesimal disc.
Keywords
This publication has 12 references indexed in Scilit:
- Nonlinear desingularization in certain free-boundary problemsCommunications in Mathematical Physics, 1980
- Asymptotic estimates for the plasma problemDuke Mathematical Journal, 1980
- Asymptotic estimates for an axisymmetric rotating fluidJournal of Functional Analysis, 1980
- The shape of axisymmetric rotating fluidJournal of Functional Analysis, 1980
- On nonlinear desingularizationBulletin of the American Mathematical Society, 1980
- Existence of axisymmetric equilibrium figuresArchive for Rational Mechanics and Analysis, 1977
- The alliance of practical and analytical insights into the nonlinear problems of fluid mechanicsPublished by Springer Nature ,1976
- A global theory of steady vortex rings in an ideal fluidActa Mathematica, 1974
- Handbook of Elliptic Integrals for Engineers and ScientistsMathematics of Computation, 1972
- Variational solutions of some nonlinear free boundary problemsArchive for Rational Mechanics and Analysis, 1971