A codimension-two stable manifold of near soliton equivariant wave maps

Abstract

We consider finite-energy equivariant solutions for the wave map problem from ${ℝ}^{2+1}$ to ${\mathbb{S}}^2$ 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.