Global well-posedness and scattering for the defocusing $\dot{H}^{\frac{1}{2}}$-critical nonlinear Schrödinger equation in $\mathbb{R}^2$

Fuente: arXiv
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Autor principal: Yu, Xueying
Formato: Preprint
Publicado: 2018
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author Yu, Xueying
author_facet Yu, Xueying
contents In this paper we consider the Cauchy initial value problem for the defocusing quintic nonlinear Schrödinger equation in $\mathbb{R}^2$ with general data in the critical space $\dot{H}^{\frac{1}{2}} (\mathbb{R}^2)$. We show that if a solution remains bounded in $\dot{H}^{\frac{1}{2}} (\mathbb{R}^2)$ in its maximal interval of existence, then the interval is infinite and the solution scatters.
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id arxiv_https___arxiv_org_abs_1805_03230
institution arXiv
publishDate 2018
record_format arxiv
spellingShingle Global well-posedness and scattering for the defocusing $\dot{H}^{\frac{1}{2}}$-critical nonlinear Schrödinger equation in $\mathbb{R}^2$
Yu, Xueying
Analysis of PDEs
In this paper we consider the Cauchy initial value problem for the defocusing quintic nonlinear Schrödinger equation in $\mathbb{R}^2$ with general data in the critical space $\dot{H}^{\frac{1}{2}} (\mathbb{R}^2)$. We show that if a solution remains bounded in $\dot{H}^{\frac{1}{2}} (\mathbb{R}^2)$ in its maximal interval of existence, then the interval is infinite and the solution scatters.
title Global well-posedness and scattering for the defocusing $\dot{H}^{\frac{1}{2}}$-critical nonlinear Schrödinger equation in $\mathbb{R}^2$
topic Analysis of PDEs
url https://arxiv.org/abs/1805.03230