On wave systems with antisymmetric potential in dimension d >= 4 and well-posedness for (half-)wave maps

Abstract

We prove a priori estimates for wave systems of the type \[ \partial_{tt} u - Δu = Ω\cdot du + F(u) \quad \text{in ${\mathbb{R}}^d\times \mathbb{R}$} \] where $d\ge 4$ and $\Omega$ is a suitable antisymmetric potential. We show that the assumptions on $\Omega$ are applicable to wave- and half-wave maps, the latter by means of the Krieger-Sire reduction. We thus obtain well-posedness of those equations for small initial data in ${\dot{H}}^{\frac{d}{2}}({\mathbb{R}}^d)$.