"Spectral Theory and Mathematical Physics"
In honor of Vladimir Georgescu
Cergy-Pontoise, June 21-24, 2016.
Photo Credit: Cergy - Axe majeur,
www.cergypontoise.fr/jcms/p2_85721/fr/le-patrimoine-moderne
| Program Spyros Alexakis Kaïs Ammari Jean-Marc Bouclet Jan Derezinski Clotilde Fermanian Kammerer Christian Gérard Sylvain Golénia Dietrich Häfner Matti Lassas Mathieu Lewin Jacob Schach Moller Francis Nier Victor Nistor Benoit Pausader Main page |
Benoit Pausader: Norm growth for the cubic nonlinear Schrödinger equation Abstract: This is a joint work with N. Tzvetkov. The question of whether the nonlinear cubic Schrodinger equation has solution which develop ``small scale creation'' (as measured as growth of high order Sobolev norm) is delicate. In many cases (e.g. in the Euclidean space, on the 1- dimensional torus...), it is not possible due to either scattering or complete integrability. However, when the domain is a ``cylinder'' R x T^2, this is possible. Another interesting fact is that there exists solutions whose norm H^s grows unboundedly for some 0<s<1, despite the existence of a conservation law at s=0 and s=1. |
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