Global existence and scattering for a class of nonlinear fourth-order Schrödinger equation below the energy space

DOI10.1016/j.na.2018.03.003zbMath1393.35219arXiv1706.07430OpenAlexW2650927918MaRDI QIDQ1748242

Van Duong Dinh

Publication date: 9 May 2018

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1706.07430

zbMATH Keywords

scatteringglobal well-posednessalmost conservation lawnonlinear fourth-order Schrödinger equationMorawetz inequality

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) NLS equations (nonlinear Schrödinger equations) (35Q55) Nonlinear higher-order PDEs (35G20) Lasers, masers, optical bistability, nonlinear optics (78A60) Initial value problems for nonlinear higher-order PDEs (35G25)

Related Items (5)

Random data theory for the cubic fourth-order nonlinear Schrödinger equation ⋮ Global solutions for \(H^s\)-critical nonlinear biharmonic Schrödinger equation ⋮ Dynamics of radial solutions for the focusing fourth-order nonlinear Schrödinger equations ⋮ Strong instability of standing waves for a fourth-order nonlinear Schrödinger equation with the mixed dispersions ⋮ Probabilistic Cauchy theory for the mass-critical fourth-order nonlinear Schrödinger equation

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