Vol. 6, No. 4, 2013

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

Ioan Bejenaru, Joachim Krieger and Daniel Tataru

Vol. 6 (2013), No. 4, 829–857
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.

Keywords
wave map, behavior near soliton, orbital stability
Mathematical Subject Classification 2010
Primary: 35L05, 35P25, 35Q75