On growth of Sobolev norms in linear Schrödinger equations with time dependent Gevrey potential

DOI10.1007/s10884-012-9244-7zbMath1247.35118OpenAlexW2093023231MaRDI QIDQ431119

Daoyuan Fang, Qidi Zhang

Publication date: 26 June 2012

Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10884-012-9244-7

zbMATH Keywords

Sobolev normsGevrey potentialtime dependent linear Schrödinger equation

Mathematics Subject Classification ID

Schrödinger operator, Schrödinger equation (35J10) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (13)

Growth of Sobolev norms in 1-d quantum harmonic oscillator with polynomial time quasi-periodic perturbation ⋮ Long time dynamics of Schrödinger and wave equations on flat tori ⋮ Reducibility of quantum harmonic oscillator on \(\mathbb{R}^d\) perturbed by a quasi: periodic potential with logarithmic decay ⋮ Growth of Sobolev norms for abstract linear Schrödinger equations ⋮ Bounded Sobolev norms for Klein-Gordon equations under non-resonant perturbation ⋮ Growth of Sobolev norms for unbounded perturbations of the Schrödinger equation on flat tori ⋮ On growth of Sobolev norms in time dependent linear Schrödinger equations on spheres ⋮ On time-splitting methods for nonlinear Schrödinger equation with highly oscillatory potential ⋮ Growth of Sobolev Norms for Solutions of Time Dependent Schrödinger Operators with Harmonic Oscillator Potential ⋮ On time dependent Schrödinger equations: global well-posedness and growth of Sobolev norms ⋮ Growth of Sobolev norms for linear Schrödinger operators ⋮ Semi-algebraic sets method in PDE and mathematical physics ⋮ Variable potentials and dispersive equations

Cites Work

• Unnamed Item
• KAM for the quantum harmonic oscillator
• On reducibility of Schrödinger equations with quasiperiodic in time potentials
• Bounded Sobolev norms for linear Schrödinger equations under resonant perturbations
• Expectation values of observables in time-dependent quantum mechanics
• On growth of Sobolev norms in linear Schrödinger equations with smooth time dependent potential
• Growth of Sobolev norms in linear Schrödinger equations with quasi-periodic potential
• Growth of Sobolev Norms of Solutions of Linear Schrodinger Equations on Some Compact Manifolds
• Logarithmic Bounds on Sobolev Norms for Time Dependent Linear Schrödinger Equations

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