Global Well-Posedness For Half-Wave Maps With $S^2$ and ${\mathbb{H}}^2$ Targets For Small Smooth Initial Data

Abstract

We prove global well-posedness for the half-wave map with $S^2$ target for small ${\dot{H}}^{\frac{n}{2}}\times {\dot{H}}^{\frac{n}{2}-1}$ initial data. We also prove the global well-posedness for the equation with ${\mathbb{H}}^2$ target for small smooth ${\dot{B}}_{2,1}^{\frac{n}{2}}\times {\dot{B}}_{2,1}^{\frac{n}{2}-1}$ initial data.

48 pages

Cited by in corpus (2)

• On uniqueness for half-wave maps in dimension d >= 3
• Global Well-Posedness and Soliton Resolution for the Half-Wave Maps Equation with Rational Data