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.

11 pages. Version 3 incorporated suggestions from the referee. The main argument remains unchanged, but the presentation is revised and clarified. Theorem 3.4 (which is an immediately corollary from the method of proof in the original manuscript) is new. Version 4 improved literature review

References in corpus (3)

• Dynamic of threshold solutions for energy-critical wave equation
• Global dynamics away from the ground state for the energy-critical nonlinear wave equation
• Threshold phenomenon for the quintic wave equation in three dimensions

Cited by in corpus (2)

• On blowup in supercritical wave equations
• Strichartz estimates in similarity coordinates and stable blowup for the critical wave equation