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A global theory of steady vortex rings in an ideal fluid

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Outgoing claims: the papers this work cites, builds on, or argues with.

inferredcites →https://doi.org/10.1002/cpa.3160120405openalex-snapshot
Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
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Maximum Principles in Differential Equations
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On Elliptic Partial Differential Equations
inferredcites →https://doi.org/10.1007/bf01181194openalex-snapshot
�ber einige Existenzprobleme der Hydrodynamik
inferredcites →https://doi.org/10.1007/bf01506223openalex-snapshot
�ber einige Existenzprobleme der Hydrodynamik homogener, unzusammendr�ckbarer, reibungsloser Fl�ssigkeiten und die Helmholtzschen Wirbels�tze
inferredcites →https://doi.org/10.1007/bf02684590openalex-snapshot
Quasi-conformal mappings in n -space and the rigidity of hyperbolic space forms
inferredcites →https://doi.org/10.1016/s0079-6417(08)60077-3openalex-snapshot
Chapter II Application of Quantum Mechanics to Liquid Helium
inferredcites →https://doi.org/10.1017/s0022112072001107openalex-snapshot
Examples of steady vortex rings of small cross-section in an ideal fluid
inferredcites →https://doi.org/10.1017/s0022112073001266openalex-snapshot
A family of steady vortex rings
inferredcites →https://doi.org/10.1017/s0305004100047083openalex-snapshot
A steady vortex ring close to Hill's spherical vortex
inferredcites →https://doi.org/10.1090/mmono/007openalex-snapshot
Applications of functional analysis in mathematical physics
inferredcites →https://doi.org/10.1090/s0002-9947-1973-0341210-xopenalex-snapshot
Critical Point Theory for Nonlinear Eigenvalue Problems with Indefinite Principal Part
inferredcites →https://doi.org/10.1098/rspa.1970.0065openalex-snapshot
On steady vortex rings of small cross-section in an ideal fluid
inferredcites →https://doi.org/10.1098/rsta.1893.0020openalex-snapshot
XX. The potential of an anchor ring.-Part II
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VI. On a spherical vortex
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Stochastic theory of the nucleation of quantized vortices in superfluid helium
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XV. Researches on the theory of vortex rings.—Part II
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Isoperimetric Inequalities in Mathematical Physics. (AM-27)
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Über Integrale der hydrodynamischen Gleichungen, welche den Wirbelbewegungen entsprechen.

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

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Existence of Helical Symmetry Vortex Patch with Small Cross-Section for the Incompressible Euler Equations In $\Mathbb R^3$
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Das Cauchyproblem der Helmholtzschen Wirbelgleichung mit einer Differenzennäherung
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The Uniqueness of Hill’s Spherical Vortex
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Vortices in Ideal Fluids
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Vortex Rings
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Probl�mes elliptiques � fronti�re libre axi-sym�triques: Estimation du diam�tre de la section au moyen de la capacit�
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A non-linear eigenvalue problem: The shape at equilibrium of a confined plasma
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Nonlinear desingularization in certain free-boundary problems
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Applications de l’analyse convexe au calcul des variations
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Global free boundary problems and the calculus of variations in the large
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Vanishing viscosity limit for a smoke ring with concentrated vorticity
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Uniqueness of Axisymmetric Viscous Flows Originating from Positive Linear Combinations of Circular Vortex Filaments
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Existence of Steady Symmetric Vortex Patch in a Disk
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Time Evolution of Concentrated Vortex Rings
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Steady Vortex Rings in a Uniform Flow and Rearrangements of a Function
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Global time evolution of concentrated vortex rings
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Remarks on a paper by Gavrilov: Grad–Shafranov equations, steady solutions of the three dimensional incompressible Euler equations with compactly supported velocities, and applications
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A Dynamical Systems Approach Towards Isolated Vorticity Regions for Tsunami Background States
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Piecewise Smooth Stationary Euler Flows with Compact Support Via Overdetermined Boundary Problems
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Optimal control of higher order elliptic distributed systems with a spectral parameter and discontinuous nonlinearity
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The dynamics of vortex rings: Leapfrogging, choreographies and the stability problem
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On solutions to the Goldshtik problem
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On the Steady Axisymmetric Vortex Rings for 3D Incompressible Euler Flows
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An Elliptic Problem Related to Planar Vortex Pairs
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Towards a complexity measure theory for vortex tangles
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Construction of axisymmetric steady states of an inviscid incompressible fluid by spatially discretized equations for pseudo‐advected vorticity
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On Stable Plane Vortex Flows of an Ideal Fluid
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Co-rotating vortices with N fold symmetry for the inviscid surface quasi-geostrophic equation
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A free boundary eigenvalue problem
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A finite element BFGS algorithm for the reconstruction of the flow field generated by vortex rings
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Finite-Amplitude Steady Waves in Stratified Fluids.
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Critical points and nonlinear variational problems
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Solutions to the two-dimensional steady incompressible Euler equations in an annulus
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Stability results for discontinuous nonlinear elliptic and parabolic problems with a S-shaped bifurcation branch of stationary solutions
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Vortex rings for the Gross-Pitaevskii equation
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Multiple Vortices for the Shallow Water Equation in Two Dimensions
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Regularization of point vortices for the Euler equation in dimension two, part II
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Multiple Vortices for the Shallow Water Equation
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Uniqueness of planar vortex patch in incompressible steady flow
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Smooth travelling-wave solutions to the inviscid surface quasi-geostrophic equation
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Desingularization of vortex rings in 3 dimensional Euler flows: with swirl
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Asymptotic behavior of global vortex rings
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Tamped functions: A rearrangement in dimension 1
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Desingularization of steady vortex of perturbation type in the lake equations
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A monotone iteration for axisymmetric vortices with swirl
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Some discontinuous variational problems
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Quasi-geostrophic vortices and their desingularization
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