Optimal blowup stability for three-dimensional wave maps

TL;DR

This paper proves the asymptotic stability of a known self-similar wave map in 3D Minkowski space under small perturbations in a fractional Sobolev space, using Strichartz estimates for a radial wave equation.

Contribution

It establishes stability results for wave maps in a fractional Sobolev space, extending previous work to more general perturbations.

Findings

Proved asymptotic stability of a self-similar wave map.

Developed Strichartz estimates for a radial wave equation with potential.

Extended stability analysis to fractional Sobolev spaces.

Abstract

We study corotational wave maps from $(1+3)$-dimensional Minkowski space into the three-sphere. We establish the asymptotic stability of an explicitly known self-similar wave map under perturbations that are small in the critical Sobolev space. This is accomplished by proving Strichartz estimates for a radial wave equation with a potential in similarity coordinates. Compared to earlier work, the main novelty lies with the fact that the critical Sobolev space is of fractional order.