Singularity formation for the higher dimensional Skyrme model

TL;DR

This paper proves that singularities can form in the classical 5+1 dimensional co-rotational Skyrme model, with solutions developing finite-time blowup at a self-similar rate, extending understanding of singularity formation in higher-dimensional field theories.

Contribution

It demonstrates finite-time singularity formation in the 5+1 dimensional Skyrme model using self-similar solutions and constructs initial data leading to gradient blowup.

Findings

Singularities form in finite time within the model.

Blowup occurs at a self-similar rate.

The singularity profile matches the self-similar solution.

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.