A codimension two stable manifold of near soliton equivariant wave maps
  We consider finite energy equivariant solutions for the wave map problem from R2+1 to S2 which are close to the soliton family. We prove asymptotic orbital stability for a codimension two class of initial data which is small with respect to a stronger topology than the energy. 
Ioan Bejenaru, Joachim Krieger, Daniel Tataru
math.AP