Bounds on the growth of high Sobolev norms of solutions to 2D Hartree equations

DOI10.3934/dcds.2012.32.3733zbMath1247.35116arXiv1003.5709OpenAlexW3102114299MaRDI QIDQ445236

Vedran Sohinger

Publication date: 24 August 2012

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1003.5709

zbMATH Keywords

nonlinear Schrödinger equationresonant decompositionHartree equationgrowth of high Sobolev norms

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) PDEs in connection with quantum mechanics (35Q40)

Related Items (13)

Local well-posedness for 2-D Schrödinger equation on irrational tori and bounds on Sobolev norms ⋮ On the growth of Sobolev norms for NLS on 2- and 3-dimensional manifolds ⋮ Growth of Sobolev norms for the analytic NLS on \(\mathbb{T}^2\) ⋮ \(\log\)-\(\log\) blow up solutions blow up at exactly \(m\) points ⋮ Strong ill-posedness for fractional Hartree and cubic NLS equations ⋮ Derivation of the 2d Gross-Pitaevskii equation for strongly confined 3d bosons ⋮ Growth of Sobolev norms and strong convergence for the discrete nonlinear Schrödinger equation ⋮ Strong nonlinear instability and growth of Sobolev norms near quasiperiodic finite gap tori for the 2D cubic NLS equation ⋮ The stability of nonlinear Schrödinger equations with a potential in high Sobolev norms revisited ⋮ Growth of Sobolev norms in the cubic nonlinear Schrödinger equation with a convolution potential ⋮ The modified energy technique and applications ⋮ A note on growth of Sobolev norms near quasiperiodic finite-gap tori for the 2D cubic NLS equation ⋮ Stability of the Cubic Nonlinear Schrodinger Equation on an Irrational Torus

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