Existence of steady vortex rings in an ideal fluid
From MaRDI portal
Publication:5899706
DOI10.1007/BF01053458zbMath0694.76012MaRDI QIDQ5899706
Antonio Ambrosetti, Michael Struwe
Publication date: 1989
Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)
a priori estimatesfree boundary problemexistence of a solutionapproximate problem``mountain pass critical pointbounded, symmetric vortex corenontrivial, cylindrically symmetric solutionssemilinear Dirichlet boundary value problemStokes stream functionvariational characterization of the ``mountain pass solution
Related Items
Vanishing viscosity limit for concentrated vortex rings, Vortex patch problem for steady lake equation, Rotating vortex patches for the planar Euler equations in a disk, Remarks on orbital stability of steady vortex rings, Travelling helices and the vortex filament conjecture in the incompressible Euler equations, Unnamed Item, On the existence of bounded Palais–Smale sequences and application to a Landesman–Lazer-type problem set on ℝN, Clustered travelling vortex rings to the axisymmetric three-dimensional incompressible Euler flows, The singular set of higher dimensional unstable obstacle type problems, Sign-changing solutions for a modified nonlinear Schrödinger equation in \(\mathbb{R}^N\), Local uniqueness of vortices for 2D steady Euler flow in a bounded domain, Remarks on the equilibrium shape of a Tokamak plasma, Vanishing viscosity limit for a smoke ring with concentrated vorticity, Unnamed Item, Nested axi-symmetric vortex rings, Existence and numerical modelling of vortex rings with elliptic boundaries, Asymptotic behaviour of global vortex rings, Critical points and nonlinear variational problems, Unnamed Item, On the singularities of a free boundary through Fourier expansion, Global vortex rings and asymptotic behaviour, Axisymmetric magnetic vortices with swirl, Multiple solutions for an elliptic problem related to vortex pairs, Desingularization of vortex rings in 3 dimensional Euler flows, Vanishing viscosity limit for an incompressible fluid with concentrated vorticity, Existence and multiplicity results for elliptic problems with critical growth and discontinuous nonlinearities, Vortex rings for the Gross-Pitaevskii equation, Regularization of point vortices pairs for the Euler equation in dimension two, Planar vortex patch problem in incompressible steady flow, A steady Euler flow with compact support, Steady vortex patches with opposite rotation directions in a planar ideal fluid, Multi-peak solutions to two types of free boundary problems, Existence of steady vortex rings in an ideal fluid, Existence of steady symmetric vortex patch in a disk, On the vortex filament conjecture for Euler flows, Uniqueness of axisymmetric viscous flows originating from positive linear combinations of circular vortex filaments, A monotone iteration for concentrated vortices, Galerkin's method, monotonicity and linking for indefinite Hamiltonian systems with bounded potential energy, Desingularization of vortices for the Euler equation, Normalized traveling solitary waves for a class of nonlinear half-wave equations, 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, Large smoke rings with concentrated vorticity, Steady vortex rings in a uniform flow and rearrangements of a function, Time evolution of concentrated vortex rings, Regularization of planar vortices for the incompressible flow, Time evolution of vortex rings with large radius and very concentrated vorticity, Existence of solutions for three dimensional stationary incompressible Euler equations with nonvanishing vorticity, Local uniqueness for vortex patch problem in incompressible planar steady flow, An elliptic problem with discontinuous sublinear nonlinearities in \(\mathbb{R}^{N}\), Existence of solutions with prescribed norm for semilinear elliptic equations, Global time evolution of concentrated vortex rings, Existence of vortex rings in Beltrami flows
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Some discontinuous variational problems
- The uniqueness of a family of steady vortex rings
- The uniqueness of Hill's spherical vortex
- The existence of surfaces of constant mean curvature with free boundaries
- Symmetry and related properties via the maximum principle
- On the existence of global vortex rings
- Variational methods for non-differentiable functionals and their applications to partial differential equations
- Finite-amplitude steady waves in stratified fluids
- A global theory of steady vortex rings in an ideal fluid
- Dual variational methods in critical point theory and applications
- Lusternik-Schnirelman theory on Banach manifolds
- A family of steady vortex rings
