Energy dispersed large data wave maps in 2+1 dimensions

TL;DR

This paper investigates the behavior of large data wave maps from 2+1 dimensional spacetime into a compact manifold, establishing conditions under which regularity and dispersive bounds are maintained.

Contribution

It proves that regularity persists for large data wave maps as long as certain bulk concentration phenomena are absent, advancing understanding of wave map dynamics.

Findings

Regularity and dispersive bounds are maintained under specific conditions.

Absence of bulk concentration prevents singularity formation.

Provides foundational results for full regularity theory in a companion work.

Abstract

In this article we consider large data Wave-Maps from $\mathbb{R}^{2+1}$ into a compact Riemannian manifold $(\mathcal{M},g)$, and we prove that regularity and dispersive bounds persist as long as a certain type of bulk (non-dispersive) concentration is absent. In a companion article we use these results in order to establish a full regularity theory for large data Wave-Maps.