Scattering for the focusingL2-supercritical andḢ2-subcritical biharmonic NLS equations

DOI10.1080/03605302.2015.1116556zbMath1342.35335arXiv1504.02853OpenAlexW2270861490MaRDI QIDQ2810597

Qing Guo

Publication date: 3 June 2016

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1504.02853

zbMATH Keywords

scatteringfocusingNLSbiharmonic

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) A priori estimates in context of PDEs (35B45) NLS equations (nonlinear Schrödinger equations) (35Q55) PDEs in connection with quantum mechanics (35Q40) Lasers, masers, optical bistability, nonlinear optics (78A60) Variational methods for higher-order elliptic equations (35J35)

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Cites Work

• Unnamed Item
• Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrödinger equations of fourth order in dimensions \(d\geqslant 9\)
• The linear profile decomposition for the fourth order Schrödinger equation
• The focusing energy-critical fourth-order Schrödinger equation with radial data
• Global well-posedness, scattering and blow-up for the energy-critical, focusing, nonlinear Schrö\-dinger equation in the radial case
• The cubic fourth-order Schrödinger equation
• Global well-posedness and scattering for the focusing energy-critical nonlinear Schrödinger equations of fourth order in the radial case
• Stability of solitons described by nonlinear Schrödinger-type equations with higher-order dispersion
• The Cauchy problem for the fourth-order nonlinear Schrödinger equation related to the vortex filament
• Wellposedness for the fourth order nonlinear Schrödinger equations
• A sharp condition for scattering of the radial 3D cubic nonlinear Schrödinger equation
• THE MASS-CRITICAL FOURTH-ORDER SCHRÖDINGER EQUATION IN HIGH DIMENSIONS
• Self-Focusing with Fourth-Order Dispersion
• Modified wave operators for the fourth-order non-linear Schrödinger-type equation with cubic non-linearity
• Inhomogeneous Strichartz estimates for the Schrödinger equation
• Endpoint Strichartz estimates
• Critical exponents and collapse of nonlinear Schr dinger equations with anisotropic fourth-order dispersion
• INHOMOGENEOUS STRICHARTZ ESTIMATES
• Inhomogeneous Strichartz estimates
• On the defect of compactness for the Strichartz estimates of the Schrödinger equations