Singularity formation for the higher dimensional Skyrme model

2024/08/27 by McNulty, Michael · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2408.15345

Abstract

This paper demonstrates that singularities form in the classical (5+1)-dimensional, co-rotational Skyrme model. It was recently proven by Chen, Schörkhuber, 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.

Cited by

• Stable Self-Similar Blow-Up In Nonlinear Wave Equations With Quadratic Time-Derivative Nonlinearities

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