On collapsing ring blow up solutions to the mass supercritical NLS

By F. Merle, Pierre Raphael, Jérémie Szeftel. 2012

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We consider the nonlinear Schr\"odinger equation $i\pa_tu+\Delta u+u|u|^{p-1}=0$ in dimension N≥2 and in the mass super critical and energy subcritical range 1+4N<p<min{N+2N−2,5}. For initial data u0∈H1 with radial symmetry, we prove a universal upper bound on the blow up speed. We then prove that this bound is sharp and attained on a family of collapsing ring blow up solutions first formally predicted by Gavish, Fibich and Wang.

Subfields: Applied Mathematics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/af5afb7ca504a2a3bffe72f25f338b3665dbc07a