Eugene Eyeson, Silvino Reyes Farina, Armin Schikorra
Extending an argument by Shatah and Struwe we obtain uniqueness for solutions of the half-wave map equation in dimension $d \geq 3$ in the natural energy class.
This paper contains 9 sections, 32 theorems, 202 equations.
Theorem 1.1
Let $d \geq 3$ and $\alpha \in (1,d+\frac{1}{2})$. If ${\bf u},{\bf v}: \mathbb{R}^d \times [0,T] \to {\mathbb S}^2$ are smooth solutions to the half-wave map equation with the same initial data ${\bf u}(\cdot,0) = {\bf v}(\cdot,0) \in Q+ C_c^\infty(\mathbb{R}^d,\mathbb{R}^3)$ for some $Q \in {\mat then ${\bf u} \equiv {\bf v}$.
