KAM for vortex patches
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Publication:6612705
DOI10.1134/s1560354724540013MaRDI QIDQ6612705
Publication date: 1 October 2024
Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)
Euler equationsquasi-periodic solutionvortex patchesperturbative symplectic reductionquasi-linear Hamiltonian equationDarboux-Caratheodory theoremzero normal mode frequency
Vortex flows for incompressible inviscid fluids (76B47) Nearly integrable Hamiltonian systems, KAM theory (70H08) Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics (70H15) Euler equations (35Q31)
Cites Work
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- KAM for autonomous quasi-linear perturbations of mKdV
- Bifurcation of rotating patches from Kirchhoff vortices
- A KAM algorithm for the resonant non-linear Schrödinger equation
- The stability of rotating vortex patches
- Degenerate KAM theory for partial differential equations
- The planetary \(N\)-body problem: symplectic foliation, reductions and invariant tori
- A KAM theorem for Hamiltonian partial differential equations with unbounded perturbations
- Asymmetrical three-dimensional travelling gravity waves
- KAM for the nonlinear beam equation
- Hamiltonian perturbations of infinite-dimensional linear systems with an imaginary spectrum
- Reducible KAM tori for the Degasperis-Procesi equation
- A KAM theorem for Hamiltonian partial differential equations in higher dimensional spaces
- Periodic and quasi-periodic solutions of nonlinear wave equations via KAM theory
- KAM for the nonlinear Schrödinger equation
- Nonlinear stability of circular vortex patches
- Motions of vortex patches
- Quasi-periodic solutions of Hamiltonian perturbations of 2D linear Schrödinger equations
- Mathematical theory of incompressible nonviscous fluids
- Dynamics near an unstable Kirchhoff ellipse
- Détermination rigoureuse des ondes permanentes d'ampleur finie.
- On the stability of certain vortex motions.
- Vorlesungen über mathematische Physik. I. Mechanik.
- KAM tori for 1D nonlinear wave equations with periodic boundary conditions
- Invariant tori in non-degenerate nearly integrable Hamiltonian systems
- Reducibility of first order linear operators on tori via Moser's theorem
- Uniformly rotating analytic global patch solutions for active scalars
- An a posteriori KAM theorem for whiskered tori in Hamiltonian partial differential equations with applications to some ill-posed equations
- Global regularity for vortex patches
- Invariant Cantor manifolds of quasi-periodic oscillations for a nonlinear Schrödinger equation
- Quasi-periodic solutions for a nonlinear wave equation
- Quasi-periodic solutions with Sobolev regularity of NLS on \(\mathbb T^d\) with a multiplicative potential
- Time quasi-periodic gravity water waves in finite depth
- Full description of Benjamin-Feir instability of Stokes waves in deep water
- Non-uniqueness of Leray solutions of the forced Navier-Stokes equations
- Quasi-periodic solutions of nonlinear wave equations on the \(d\)-dimensional torus
- Quasi-periodic incompressible Euler flows in 3D
- Quasi-periodic solutions for fully nonlinear forced reversible Schrödinger equations
- Gravity capillary standing water waves
- Boundary regularity of rotating vortex patches
- KAM for reversible derivative wave equations
- Diophantine approximations on submanifolds of Euclidean space
- Fourier integral operators. II
- Standing waves on an infinitely deep perfect fluid under gravity
- Large KAM tori for quasi-linear perturbations of KdV
- Traveling quasi-periodic water waves with constant vorticity
- Quasi-periodic solutions to the incompressible Euler equations in dimensions two and higher
- Vorticity and incompressible flow
- A Nash-Moser Approach to KAM Theory
- KAM theory for the Hamiltonian derivative wave equation
- KAM tori for reversible partial differential equations
- Persistance de structures géométriques dans les fluides incompressibles bidimensionnels
- Small divisor problem in the theory of three-dimensional water gravity waves
- Nonlinear Stability of Vortex Patches
- Formation of singularities for wave equations including the nonlinear vibrating string
- Generalized implicit function theorems with applications to some small divisor problems, II
- Newton's method and periodic solutions of nonlinear wave equations
- Traveling Two and Three Dimensional Capillary Gravity Water Waves
- Existence of small loops in a bifurcation diagram near degenerate eigenvalues
- Green's Function Estimates for Lattice Schrodinger Operators and Applications. (AM-158)
- KAM theory without action-angle variables
- Quasi-periodic solutions of the 2D Euler equation
- Traveling water waves — the ebb and flow of two centuries
- Quasi-Periodic Standing Wave Solutions of Gravity-Capillary Water Waves
- Global Bifurcation of Rotating Vortex Patches
- Démonstration du ‘théorème d'Arnold’ sur la stabilité du système planétaire (d'après Herman)
- PROOF OF A THEOREM OF A. N. KOLMOGOROV ON THE INVARIANCE OF QUASI-PERIODIC MOTIONS UNDER SMALL PERTURBATIONS OF THE HAMILTONIAN
- Development of Singularities of Solutions of Nonlinear Hyperbolic Partial Differential Equations
- Non-stationary flow of an ideal incompressible liquid
- Nash-Moser theory for standing water waves.
- Periodic and quasi-periodic Euler-\( \alpha\) flows close to Rankine vortices
- Time quasi-periodic vortex patches of Euler equation in the plane
- Quasi-Periodic Traveling Waves on an Infinitely Deep Perfect Fluid Under Gravity
- Pure gravity traveling quasi‐periodic water waves with constant vorticity
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