Global Well-Posedness and Soliton Resolution for the Half-Wave Maps Equation with Rational Data

Patrick Gérard, Enno Lenzmann

We study the energy-critical half-wave maps equation: \[ \partial_t \mathbf{u} = \mathbf{u} \times |D| \mathbf{u} \] for $\mathbf{u}:[0,T)\times \mathbb{R}\to {\mathbb{S}}^2$. O…