Global existence and asymptotic behavior of small solutions to nonlinear Schrödinger equations in 3D.
type: Item
instance of: scholarly article
title: Global existence and asymptotic behavior of small solutions to nonlinear Schrödinger equations in 3D.
zbMATH Open document ID: 1212.35451
author: Yuichiro Kawahara
published in: Differential and Integral Equations
publication date: 2010-06-15T00:00:00Z
review text: A nonlinear Schrödinger equation is studied. It is shown that for the solution \(u=u(x,t)\) there exists a unique state \(u_{\infty }\) such that \[ \| u(t) - \text{e}^{\frac {\text{i}t}{2}}u_{\infty }\| _{L^2} \leq Ct^{-\frac {5}{4}} \] for a small initial condition \(u_0\), \(\text{i}\) being the complex unit.
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 5720798
zbMATH Keywords: global existence
zbMATH Keywords: asymptotic behavior
zbMATH Keywords: small solutions
MaRDI profile type: Publication
Recommended article: Global existence of small solutions to nonlinear Schrödinger equations
Recommended article: Q4213449
Recommended article: Almost global existence of small solutions to quadratic nonlinear Schrödinger equations in three space dimensions
Recommended article: Global existence and asymptotic behavior of solutions to some nonlinear systems of Schrödinger equations
Recommended article: Global existence of small analytic solutions to nonlinear Schrödinger equations
Recommended article: Q5430046
Recommended article: Global existence of small classical solutions to nonlinear Schrödinger equations
Recommended article: Global extstence of small solutions to semiliner schrödinger equations
Recommended article: Q4796761
Recommended article: Global well-posedness of the energy-critical nonlinear Schrödinger equation with small initial data in \(H^1(\mathbb T^3)\)
description: scientific article; zbMATH DE number 5720798