Global wellposedness of hedgehog solutions for the (3+1) Skyrme model

TL;DR

This paper proves the global well-posedness of hedgehog solutions in the energy-supercritical (3+1)-dimensional Skyrme model using a novel approach applicable to large initial data.

Contribution

It introduces a new strategy to establish global well-posedness for large initial data in the energy-supercritical Skyrme model.

Findings

Global well-posedness for arbitrarily large initial data

New analytical strategy for energy-supercritical problems

Applicable to hedgehog solutions in (3+1) dimensions

Abstract

We consider the dynamics of hedgehog solutions in the $(3+1)$-dimensional Skyrme model which is an energy-supercritical problem. We introduce a new strategy to prove global wellposedness for arbitrarily large initial data.