Strichartz estimates in similarity coordinates and stable blowup for the critical wave equation

Abstract

We establish Strichartz estimates in similarity coordinates for the radial wave equation in three spatial dimensions with a (time-dependent) self-similar potential. As an application we consider the critical wave equation and prove the asymptotic stability of the ODE blowup profile in the energy space.

39 pages, referees' suggestions incorporated, typos fixed, more references added; will appear in Duke Math. J

References in corpus (5)

• Construction of type II blow-up solutions for the energy-critical wave equation in dimension 5
• On blowup in supercritical wave equations
• Exotic blowup solutions for the u^5 focusing wave equation in R^3
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Cited by in corpus (10)

• Dynamical behavior near explicit self-similar blow up solutions for the Born-Infeld equation
• The blow-up rate for a non-scaling invariant semilinear heat equation
• Stable ODE-type blowup for some quasilinear wave equations with derivative-quadratic nonlinearities
• On the existence and stability of blowup for wave maps into a negatively curved target
• The blow-up rate for a non-scaling invariant semilinear wave equations in higher dimensions
• Blowup stability at optimal regularity for the critical wave equation
• On blow-up for the supercritical defocusing nonlinear wave equation
• Optimal blowup stability for three-dimensional wave maps
• Sharp universal rate for stable blow-up of corotational wave maps
• Self-similar solutions of energy-supercritical focusing wave equations in all dimensions