Global well-posedness and scattering for the fourth order nonlinear Schrödinger equations with small data in modulation and Sobolev spaces

DOI10.1016/j.matpur.2015.09.005zbMath1336.35322OpenAlexW1424122346MaRDI QIDQ897832

Michael Ruzhansky, Hua Zhang, Bao Xiang Wang

Publication date: 7 December 2015

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matpur.2015.09.005

zbMATH Keywords

global well-posednesssmall initial datafourth order nonlinear Schrödinger equationsmodulation and Sobolev spaces

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Function spaces arising in harmonic analysis (42B35) NLS equations (nonlinear Schrödinger equations) (35Q55) Harmonic analysis and PDEs (42B37)

Related Items (23)

Norm estimates for \(\tau\)-pseudodifferential operators in Wiener amalgam and modulation spaces ⋮ On Fourier integral operators with Hölder-continuous phase ⋮ The probabilistic Cauchy problem for the fourth order Schrödinger equation with special derivative nonlinearities ⋮ Decay estimates and Strichartz estimates of fourth-order Schrödinger operator ⋮ Retracted: The probabilistic Cauchy problem for the fourth order Schrödinger equation with special derivative nonlinearities ⋮ Dynamics of the nonlinear Klein-Gordon equation in the nonrelativistic limit ⋮ The Cauchy problem for the generalized Zakharov-Kuznetsov equation on modulation spaces ⋮ Well‐posedness of generalized KdV and one‐dimensional fourth‐order derivative nonlinear Schrödinger equations for data with an infinite L² norm ⋮ Almost sure global well-posedness for the fourth-order nonlinear Schrödinger equation with large initial data ⋮ Boundedness of iterated spherical average on modulation spaces ⋮ The Hartree–Fock equations in modulation spaces ⋮ Almost diagonalization of \(\tau \)-pseudodifferential operators with symbols in Wiener amalgam and modulation spaces ⋮ Dispersive estimates for inhomogeneous fourth-order Schrödinger operator in 3D with zero energy obstructions ⋮ Random data Cauchy problem for the fourth order Schrödinger equation with the second order derivative nonlinearities ⋮ Local well-posedness for the derivative nonlinear Schrödinger equation with \(L^2\)-subcritical data ⋮ Well-posedness for the fourth-order Schrödinger equation with third order derivative nonlinearities ⋮ On a fourth‐order nonlinear Helmholtz equation ⋮ A characterization of modulation spaces by symplectic rotations ⋮ The initial-boundary value problem for the biharmonic Schrödinger equation on the half-line ⋮ Almost Diagonalization of Pseudodifferential Operators ⋮ Global solution for a sixth-order nonlinear Schrödinger equation ⋮ Well-posedness of the initial-boundary value problem for the fourth-order nonlinear Schrödinger equation ⋮ Entire solutions of certain fourth order elliptic problems and related inequalities

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