On the regularity of the 2+1 dimensional Skyrme model

TL;DR

This paper investigates the regularity of solutions in the 2+1 dimensional Skyrme model, proving that energy does not concentrate, which is essential for establishing global regularity.

Contribution

It introduces a method using multipliers to prove non-concentration of energy in equivariant Skyrme maps, advancing the understanding of solution regularity.

Findings

Energy does not concentrate in 2+1 dimensional equivariant Skyrme maps

Method of multipliers effectively proves regularity properties

Progress towards a global regularity theory for the Skyrme model

Abstract

One of the most interesting open problems concerning the Skyrme model of nuclear physics is the regularity of its solutions. In this article, we study 2+1 dimensional equivariant Skyrme maps, for which we prove, using the method of multipliers, that the energy does not concentrate. This is one of the crucial steps towards a global regularity theory.