Non-dispersive vanishing and blow up at infinity for the energy critical   nonlinear Schr\"odinger equation in R^3
  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 $t^{\nu}$. 
Cecilia Ortoleva, Galina Perelman (LAMA)
math.AP