Global wellposedness of defocusing critical nonlinear Schrödinger equation in the radial case期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Global wellposedness of defocusing critical nonlinear Schrödinger equation in the radial case

Authors:	J Bourgain

Institution:	School of Mathematics, Institute for Advanced Study, Princeton, New Jersey 08540

Abstract:	We establish global wellposedness and scattering for the $H^{1}$ -critical defocusing NLS in 3D $\begin{equation}iu_{t}+\Delta u - u\|u\|^{4}=0 \end{equation}$ assuming radial data $\phi \in H^{s}$ , $s\geq 1$ . In particular, it proves global existence of classical solutions in the radial case. The same result is obtained in 4D for the equation $\begin{equation}iu_{t}+\Delta u -u\|u\|^{2} =0. \end{equation}$

Keywords:	Nonlinear Schr\"{o}dinger equation global wellposedness

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