Time quasi-periodic vortex patches of Euler equation in the plane

2023/05/23 by Massimiliano Berti, Zineb Hassainia, Nader Masmoudi · 38 citations
Mathematics · Physics and Astronomy · #Angular momentum #Astro and Planetary Science #Classical mechanics #Hamiltonian (control theory) #Hamiltonian system #Magnetic confinement fusion research #Mathematical analysis #Mathematical physics #Mathematics #Physics #Quantum chaos and dynamical systems #Symplectic geometry

paper · doi:10.1007/s00222-023-01195-4

published in Inventiones mathematicae 233(3), 1279-1391 (Springer Science+Business Media)

openalex publication_date 2023/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Citations

• Periodic and quasi-periodic solutions of nonlinear wave equations via KAM theory
• KAM for Reversible Derivative Wave Equations
• Invariant Cantor Manifolds of Quasi-Periodic Oscillations for a Nonlinear Schrodinger Equation
• Fourier integral operators. II

Cited by

• Long time dynamics of space periodic water waves
• Two-Point Vortex Confinement in a simply connected domain
• Dynamics of Ideal Fluid Flows
• Invariant sets through resonant normal form for infinite dimensional holomorphic vector fields
• Stability of Lamb dipoles for odd-symmetric and non-negative initial disturbances without the finite mass condition
• Long-wave instability of periodic shear flows for the 2D Navier-Stokes equations
• Linearly Stable KAM Tori for One Dimensional Forced Kirchhoff Equations under Periodic Boundary Conditions
• Stability for multiple Lamb dipoles
• Long time confinement of multiple concentrated vortices
• On almost periodic solutions to NLS without external parameters
• Long-time dynamics for the Kelvin-Helmholtz equations close to circular vortex sheets
• Space Quasi-Periodic Steady Euler Flows Close to the Inviscid Couette Flow. [europepmc]
• A KAM Approach to the Inviscid Limit for the 2D Navier-Stokes Equations. [europepmc]
• Large Amplitude Quasi-Periodic Traveling Waves in Two Dimensional Forced Rotating Fluids. [europepmc]
• Long-Time Dynamics for the Kelvin-Helmholtz Equations Close to Circular Vortex Sheets. [europepmc]