Wave map Cauchy data
= Wave map Cauchy data
Initial position $\phi_0$ for a <wave map> takes values in the target, and initial velocity $\phi_1$ belongs to its <tangent space> at $\phi_0(x)$. For $S^2$ this means $|\phi_0|=1$ and $\phi_0\cdot\phi_1=0$. Localized data agree with a constant map and zero velocity outside a compact set; the map itself need not be a compactly supported ambient function.