Optimal blowup stability for three-dimensional wave maps

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.