Geodesic
Global wellposedness of defocusing critical nonlinear Schrödinger equation in the radial case
Bourgain, J.1
1School 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 
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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