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

TL;DR

This paper derives Strichartz estimates in similarity coordinates for the radial wave equation with a self-similar potential and uses these to prove the stability of blowup solutions in the critical wave equation.

Contribution

It introduces Strichartz estimates in similarity coordinates for a wave equation with a self-similar potential and applies them to establish stability of blowup profiles.

Findings

Strichartz estimates established in similarity coordinates.

Proved asymptotic stability of the ODE blowup profile.

Results apply to the critical wave equation in energy space.

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.