On collapsing ring blow up solutions to the mass supercritical NLS

Abstract

We consider the nonlinear Schrödinger equation $i{\partial }_{t}u+\Delta u+u|u{|}^{p-1}=0$ in dimension $N\ge 2$ and in the mass super critical and energy subcritical range $1+\frac{4}{N}<p<\min \{\frac{N+2}{N-2},5\}.$ For initial data $u_0\in H^1$ 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.

48 pages

References in corpus (1)

• Nondispersive solutions to the L2-critical half-wave equation

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