THE GLOBAL CAUCHY PROBLEM FOR THE NLS WITH HIGHER ORDER ANISOTROPIC DISPERSION

DOI10.1017/S0017089519000491zbMath1455.35234arXiv1904.00819OpenAlexW2930440724MaRDI QIDQ5140590

Leonid Chaichenets, Nikolaos Pattakos

Publication date: 16 December 2020

Published in: Glasgow Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1904.00819

zbMATH Keywords

nonlinear Schrödinger equation, global well-posedness

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) NLS equations (nonlinear Schrödinger equations) (35Q55) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (1)

Unconditional uniqueness of higher order nonlinear Schrödinger equations

Cites Work

• The global Cauchy problem for the NLS and NLKG with small rough data
• Remarks on NLS with higher order anisotropic dispersion
• Nonlinear scattering theory at low energy
• Asymptotic behavior in time of solution to the nonlinear Schrödinger equation with higher order anisotropic dispersion
• Nonlinear Schrödinger equation, differentiation by parts and modulation spaces
• The global Cauchy problems for the nonlinear dispersive equations on modulation spaces
• Modulation type spaces for generators of polynomially bounded groups and Schrödinger equations
• Remarks on nonlinear operations on modulation spaces
• Pseudo-Differential Operators and Symmetries
• Dispersion estimates for fourth order Schrödinger equations
• On well-posedness of the third-order nonlinear Schrödinger equation with time-dependent coefficients
• Solutions to nonlinear higher order Schrödinger equations with small initial data on modulation spaces

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