Blowup stability at optimal regularity for the critical wave equation

TL;DR

This paper proves the stability of blowup solutions for the 5D energy-critical wave equation by establishing Strichartz estimates in similarity coordinates, demonstrating nonlinear asymptotic stability at optimal regularity.

Contribution

It introduces Strichartz estimates in similarity coordinates for the 5D radial wave equation and proves the nonlinear stability of blowup solutions in the energy space.

Findings

Strichartz estimates established in similarity coordinates

Nonlinear asymptotic stability of ODE blowup proven

Stability results at optimal regularity in 5D

Abstract

We establish Strichartz estimates for the radial energy-critical wave equation in 5 dimensions in similarity coordinates. Using these, we prove the nonlinear asymptotic stability of the ODE blowup in the energy space.