Geodesic
Global wellposedness of defocusing critical nonlinear Schrödinger equation in the radial case
Bourgain, J.1
1 School of Mathematics, Institute for Advanced Study, Princeton, New Jersey 08540
Journal of the American Mathematical Society, Tome 12 (1999) no. 1, pp. 145-171

Voir la notice de l'article provenant de la source American Mathematical Society

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*}
DOI : 10.1090/S0894-0347-99-00283-0

Bourgain, J. 1

1 School of Mathematics, Institute for Advanced Study, Princeton, New Jersey 08540 
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Bourgain, J. Global wellposedness of defocusing critical nonlinear Schrödinger equation in the radial case. Journal of the American Mathematical Society, Tome 12 (1999) no. 1, pp. 145-171. doi: 10.1090/S0894-0347-99-00283-0

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