On type I blow up formation for the critical NLW

Abstract

We introduce a suitable concept of weak evolution in the context of the radial quintic focussing semilinear wave equation on $\mathbb{R}^{3+1}$, that is adapted to continuation past type II singularities. We show that the weak extension leads to type I singularity formation for initial data corresponding to: (i) the Kenig-Merle blow-up solutions with initial energy below the ground state and (ii) the Krieger-Nakanishi-Schlag blow-up solutions sitting initially near and "above" the ground state static solution.