Non-dispersive vanishing and blow up at infinity for the energy critical nonlinear Schrödinger equation in R^3

Abstract

We consider the energy critical focusing NLS in R^3 and prove, for any $\nu$ sufficiently small, the existence of radial finite energy solutions that as $t\to \infty$ behave as a sum of a dynamically rescaled ground state plus a radiation, the scaling law being of the form $t^{\nu }$.

References in corpus (2)

• Stable manifolds for all monic supercritical NLS in one dimension
• Slow blow-up solutions for the H^1(R^3) critical focusing semi-linear wave equation in R^3