Scattering theory for the defocusing fourth-order Schrödinger equation

DOI10.1088/0951-7715/29/2/692zbMath1337.35137arXiv1211.4668OpenAlexW3104377253MaRDI QIDQ2794866

Chang Xing Miao, Ji Qiang Zheng

Publication date: 11 March 2016

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1211.4668

zbMATH Keywords

scattering theoryStrichartz estimateDuhamel principleconcentration compactnessfourth-order Schrödinger equationcritical regularity

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) A priori estimates in context of PDEs (35B45) NLS equations (nonlinear Schrödinger equations) (35Q55) Nonlinear evolution equations (47J35) Strong solutions to PDEs (35D35)

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On the decay property of the cubic fourth-order Schrödinger equation ⋮ Asymptotic behavior in time of solution to the nonlinear Schrödinger equation with higher order anisotropic dispersion ⋮ Asymptotics for the fourth-order nonlinear Schrödinger equation in 2D ⋮ Unconditional uniqueness of solution for \(\dot{H}^{s_c}\) critical 4th order NLS in high dimensions ⋮ Asymptotics for a class of oscillating fourth-order nonlinear Schrödinger equations ⋮ Sharp well-posedness of the Cauchy problem for the fourth order nonlinear Schrödinger equation ⋮ Random data final-state problem of fourth-order inhomogeneous NLS ⋮ Global Well-Posedness and Scattering for Fourth-Order Schrödinger Equations on Waveguide Manifolds ⋮ Global and non-global solutions for a class of damped fourth-order Schrödinger equations ⋮ Dynamics of radial solutions for the focusing fourth-order nonlinear Schrödinger equations ⋮ Scattering theory for the defocusing fourth order NLS with potentials ⋮ Dispersive estimates for inhomogeneous fourth-order Schrödinger operator in 3D with zero energy obstructions ⋮ Local well-posedness for the inhomogeneous biharmonic nonlinear Schrödinger equation in Sobolev spaces

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