Formation of singularities for equivariant 2+1 dimensional wave maps   into the two-sphere
  In this paper we report on numerical studies of the Cauchy problem for equivariant wave maps from 2+1 dimensional Minkowski spacetime into the two-sphere. Our results provide strong evidence for the conjecture that large energy initial data develop singularities in finite time and that singularity formation has the universal form of adiabatic shrinking of the degree-one harmonic map from $\mathbb{R}^2$ into $S^2$. 
Piotr Bizo\'n, Tadeusz Chmaj, Zbislaw Tabor