Scattering for wave maps exterior to a ball
Analysis of PDEs
2012-10-09 v2 Mathematical Physics
math.MP
Abstract
We consider 1-equivariant wave maps from \R \times (\R^3 \setminus B) to S^3 where B is a ball centered at 0, and the boundary of B gets mapped to a fixed point on S^3. We show that 1-equivariant maps of degree zero scatter to zero irrespective of their energy. For positive degrees, we prove asymptotic stability of the unique harmonic maps in the energy class determined by the degree.
Keywords
Cite
@article{arxiv.1112.5042,
title = {Scattering for wave maps exterior to a ball},
author = {Andrew Lawrie and Wilhelm Schlag},
journal= {arXiv preprint arXiv:1112.5042},
year = {2012}
}
Comments
41 pages. Fixed minor typos. To appear in Advances in Mathematics