Global existence for the cubic nonlinear Schrödinger equation in lower order Sobolev spaces.

zbMath1249.35306MaRDI QIDQ417021

Pavel I. Naumkin, Nakao Hayashi

Publication date: 11 May 2012

Published in: Differential and Integral Equations (Search for Journal in Brave)

zbMATH Keywords

Cauchy problemasymptoticcubic nonlinear Schrödinger equation

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)

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The lifespan of small solutions to cubic derivative nonlinear Schrödinger equations in one space dimension ⋮ Long Range Scattering for Nonlinear Schrödinger Equations with Critical Homogeneous Nonlinearity ⋮ Logarithmic nature of the long-time asymptotics of solutions of a Sobolev-type nonlinear equations with cubic nonlinearities ⋮ Long-range scattering for a critical homogeneous type nonlinear Schrödinger equation with time-decaying harmonic potentials ⋮ Long-range scattering for nonlinear Schrödinger equations with critical homogeneous nonlinearity in three space dimensions ⋮ Large time asymptotic behavior of solutions to higher order nonlinear Schrödinger equation ⋮ Almost global existence for cubic nonlinear Schrödinger equations in one space dimension ⋮ Global existence of solutions for a subcritical nonlinear Schrödinger equation ⋮ On the derivative nonlinear Schrödinger equation with weakly dissipative structure

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