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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

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


Author: J. Bourgain
Journal: J. Amer. Math. Soc. 12 (1999), 145-171
MSC (1991): Primary 35Q55, 35L15.
MathSciNet review: 1626257
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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*}


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Additional Information

J. Bourgain
Affiliation: School of Mathematics, Institute for Advanced Study, Princeton, New Jersey 08540
Email: bourgain@math.ias.edu

DOI: http://dx.doi.org/10.1090/S0894-0347-99-00283-0
PII: S 0894-0347(99)00283-0
Keywords: Nonlinear Schr\"{o}dinger equation, global wellposedness.
Received by editor(s): April 20, 1998
Article copyright: © Copyright 1999 American Mathematical Society