A continuity argument for a semilinear Skyrme model

TL;DR

This paper proves that solutions to a modified wave map problem, inspired by the Skyrme model, remain continuous at the earliest potential singularity in the equivariant case, contributing to understanding singularity formation.

Contribution

It introduces a continuity argument for a semilinear Skyrme model modification, demonstrating solution regularity at initial singularities in the equivariant setting.

Findings

Solutions remain continuous at the first possible singularity.

The semilinear modification preserves regularity in the equivariant case.

Provides a new approach to analyzing singularities in wave map problems.

Abstract

We investigate a semilinear modification for the wave map problem proposed by Adkins and Nappi, and prove that in the equivariant case the solution remain continuous at the first possible singularity.