English

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

R2 v1 2026-06-21T19:55:14.093Z