Vol. 6, No. 4, 2013

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ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
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 2+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.

Keywords
wave map, behavior near soliton, orbital stability
Mathematical Subject Classification 2010
Primary: 35L05, 35P25, 35Q75
Milestones
Received: 27 September 2011
Revised: 27 August 2012
Accepted: 27 September 2012
Published: 21 August 2013
Authors
Ioan Bejenaru
Department of Mathematics
University of California at San Diego
9500 Gilman Dr.
La Jolla 92093-011
United States
Joachim Krieger
Batiment des Mathématiques
École Polytechnique F’ed’erale de Lausanne
Station 8
CH-1015 Lausanne
France
Daniel Tataru
Department of Mathematics
University of California at Berkeley
Evans Hall
Berkeley, CA 94720
United States