Singularity formation for the higher dimensional Skyrme model

Abstract

This paper demonstrates that singularities form in the classical $(5+1)$-dimensional, co-rotational Skyrme model. It was recently proven by Chen, Sch\"orkhuber, and the author that the strong field limit of the $(5+1)$-dimensional, co-rotational Skyrme model admits an explicit self-similar solution which is asymptotically stable within backwards light cones. Seeded by the limiting model, we construct an open set of initial data whose evolution within a backwards light cone, according to the full model, suffers a gradient blowup in finite time. Moreover, the singularity develops at the self-similar rate and possesses an asymptotic profile given by the self-similar profile of the strong field model.