Global well-posedness for the cubic nonlinear Schrödinger equation with initial data lying in L p-based Sobolev spaces

DOI10.1063/5.0042321zbMath1476.35233arXiv2012.14355OpenAlexW3183414141MaRDI QIDQ5009718

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Publication date: 5 August 2021

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2012.14355

zbMATH Keywords

nonlinear Schrödinger equation

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Smoothness and regularity of solutions to PDEs (35B65) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) NLS equations (nonlinear Schrödinger equations) (35Q55) Phase transitions (general) in equilibrium statistical mechanics (82B26) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Soliton solutions (35C08) Time-dependent Schrödinger equations and Dirac equations (35Q41) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items

Introduction to the Special Issue: In memory of Jean Bourgain, Global wellposedness of NLS in \(H^1(\mathbb{R}) + H^s(\mathbb{T})\), Nonlinear wave equations with slowly decaying initial data, The quasi-periodic Cauchy problem for the generalized Benjamin-Bona-Mahony equation on the real line, Local smoothing estimates of fractional Schrödinger equations in \(\alpha\)-modulation spaces with some applications, Local smoothing and Hardy spaces for Fourier integral operators on manifolds, Well-posedness for the 1D cubic nonlinear Schrödinger equation in \(L^p, p > 2\), Wellposedness of NLS in modulation spaces

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