Solution
= Solution
\b[<Harmonic maps> give nonconstant <stationary wave maps>.] For $n=2$, inverse <stereographic projection> gives
$$
Q(x)=\frac{(2x_1,2x_2,|x|^2-1)}{1+|x|^2}.
$$
It satisfies $|Q|=1$ and $\Delta Q=-|\nabla Q|^2Q$, so $\phi(t,x)=Q(x)$ is a smooth global <wave map>. Its <wave map energy> is $4\pi$, since $|\nabla Q|^2=8/(1+|x|^2)^2$. Translations and rescalings give further examples; these <harmonic maps> approach a constant at infinity.