Continuity of generalized wave maps on the sphere

TL;DR

This paper investigates a generalized wave map equation inspired by nuclear physics, demonstrating that solutions stay continuous at the origin, which is crucial for developing a regularity theory for these equations.

Contribution

It proves the continuity of solutions at the origin for a generalized wave map equation, advancing the understanding of their regularity properties.

Findings

Solutions remain continuous at the origin

First step towards regularity theory for generalized wave maps

Extension of wave map analysis to nuclear physics models

Abstract

We consider a generalization of wave maps based on the Adkins-Nappi model of nuclear physics. In particular, we show that solutions to this equation remain continuous at the origin, which is a first step towards establishing a regularity theory for this equation.