Almost global existence for some Hamiltonian PDEs with small Cauchy data on general tori

DOI10.1007/s00220-023-04899-zarXiv2208.00413OpenAlexW4391215926MaRDI QIDQ6188098

Dario Bambusi, Roberto Feola, Riccardo Montalto

Publication date: 1 February 2024

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2208.00413

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) PDEs in connection with fluid mechanics (35Q35) Stability in context of PDEs (35B35) NLS equations (nonlinear Schrödinger equations) (35Q55) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Quantum hydrodynamics and relativistic hydrodynamics (76Y05) PDEs in connection with mechanics of deformable solids (35Q74) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Cites Work

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• Birkhoff normal form for partial differential equations with tame modulus
• Transfer of energy to high frequencies in the cubic defocusing nonlinear Schrödinger equation
• On long time existence for small solutions of semi-linear Klein-Gordon equations on the torus
• On growth of Sobolev norms in linear Schrödinger equations with smooth time dependent potential
• Birkhoff normal form for some nonlinear PDEs
• Forme normale pour NLS en dimension quelconque. (Normal form for NLS in arbitrary dimension)
• Almost global solutions of capillary-gravity water waves equations on the circle
• Construction of approximative and almost periodic solutions of perturbed linear Schrödinger and wave equations
• Asymptotic stability of ground states in some Hamiltonian PDEs with symmetry
• Long-time existence for multi-dimensional periodic water waves
• Growth of Sobolev norms in the cubic defocusing nonlinear Schrödinger equation
• Long-time existence for semi-linear beam equations on irrational tori
• Quadratic life span of periodic gravity-capillary water waves
• Quadratic lifespan and growth of Sobolev norms for derivative Schrödinger equations on generic tori
• Spectral asymptotics of all the eigenvalues of Schrödinger operators on flat tori
• Sobolev norms explosion for the cubic NLS on irrational tori
• Long-time stability of the quantum hydrodynamic system on irrational tori
• An abstract Birkhoff normal form theorem and exponential type stability of the 1d NLS
• A Nekhoroshev type theorem for the derivative nonlinear Schrödinger equation
• Exponential and sub-exponential stability times for the NLS on the circle
• On the growth of Sobolev norms for NLS on 2- and 3-dimensional manifolds
• The lifespan of small data solutions in two dimensional capillary water waves
• A Nekhoroshev-type theorem for the nonlinear Schrödinger equation on the torus
• Long-time instability and unbounded Sobolev orbits for some periodic nonlinear Schrödinger equations
• Long time dynamics of Schrödinger and wave equations on flat tori
• Growth of Sobolev norms for unbounded perturbations of the Schrödinger equation on flat tori
• Sub-exponential stability for the beam equation
• Sobolev Stability of Plane Wave Solutions to the Cubic Nonlinear Schrödinger Equation on a Torus
• Long-time existence for the semilinear Klein–Gordon equation on a compact boundary-less Riemannian manifold
• Growth of Sobolev Norms of Solutions of Linear Schrodinger Equations on Some Compact Manifolds
• Bounds on the growth of high Sobolev norms of solutions to nonlinear Schroedinger equations on $\mathbb{R}$
• Long time existence for fully nonlinear NLS with small Cauchy data on the circle
• Long Time Stability of Hamiltonian Partial Differential Equations
• LONG TIME BEHAVIOR OF THE SOLUTIONS OF NLW ON THE -DIMENSIONAL TORUS
• Stability of the Cubic Nonlinear Schrodinger Equation on an Irrational Torus
• Quasi-linear perturbations of Hamiltonian Klein-Gordon equations on spheres
• Almost global existence for Hamiltonian semilinear Klein‐Gordon equations with small Cauchy data on Zoll manifolds
• Birkhoff Normal Form and Long Time Existence for Periodic Gravity Water Waves
• Long time solutions for quasilinear Hamiltonian perturbations of Schrödinger and Klein-Gordon equations on tori
• Strong nonlinear instability and growth of Sobolev norms near quasiperiodic finite gap tori for the 2D cubic NLS equation

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