Equivariant Schr\"odinger Maps in two spatial dimensions
  We consider equivariant solutions for the Schr\"odinger map problem from $\mathbb{R}^{2+1}$ to $\mathbb{S}^2$ with energy less than $4\pi$ and show that they are global in time and scatter. 
Ioan Bejenaru, Alexandru Ionescu, Carlos E. Kenig, Daniel Tataru
math.AP