Large data global regularity for the classical equivariant Skyrme model

TL;DR

This paper proves that solutions to the classical equivariant Skyrme model with large initial data remain globally regular in time, for initial data in certain Sobolev spaces.

Contribution

It establishes the global regularity for the equivariant Skyrme model with large initial data in Sobolev spaces, a significant extension over previous small-data results.

Findings

Global regularity for large data in $H^s\times H^{s-1}$ with $s>7/2$

Validity of solutions for all time without singularity formation

Extension of known results to larger initial data regimes

Abstract

This article is concerned with the large data global regularity for the equivariant case of the classical Skyrme model and proves that this is valid for initial data in $H^s\times H^{s-1}(\mathbb{R}^3)$ with $s>7/2$.