Global regularity of wave maps V. Large data local wellposedness and perturbation theory in the energy class

TL;DR

This paper proves large data local well-posedness for wave maps from 2D Minkowski space to hyperbolic spaces in the energy class, advancing understanding of their regularity and stability.

Contribution

It introduces a new large data local well-posedness result using harmonic map heat flow and specialized function spaces, filling a key gap in the series on wave map regularity.

Findings

Establishes local well-posedness for large data in the energy class.

Utilizes harmonic map heat flow and Tataru's function spaces.

Supports the broader goal of proving global regularity for wave maps.

Abstract

Using the harmonic map heat flow and the function spaces of Tataru and the author, we establish a large data local well-posedness result in the energy class for wave maps from two-dimensional Minkowski space $\R^{1+2}$ to hyperbolic spaces $\H^m$. This is one of the five claims required in an earlier paper in this series to prove global regularity for such wave maps.