Bounds on the speed of type II blow-up for the energy critical wave equation in the radial case

Abstract

We consider the focusing energy-critical wave equation in space dimension $N\in \{3,4,5\}$ for radial data. We study type II blow-up solutions which concentrate one bubble of energy. It is known that such solutions decompose in the energy space as a sum of the bubble and an asymptotic profile. We prove bounds on the blow-up speed in the case when the asymptotic profile is sufficiently regular. These bounds are optimal in dimension $N=5$. We also prove that if the asymptotic profile is sufficiently regular, then it cannot be strictly negative at the origin.

22 pages

Cited by in corpus (3)

• Strichartz estimates in similarity coordinates and stable blowup for the critical wave equation
• Stable ODE-type blowup for some quasilinear wave equations with derivative-quadratic nonlinearities
• Non-flat conformal blow-up profiles for the 1D critical nonlinear Schrödinger equation