Scattering for wave maps exterior to a ball

Details Scattering for wave maps exterior to a ball Scattering for wave maps exterior to a ball

2011-12-21

arxiv.org/abs/1112.5042v1

Mathematics

Analysis of PDEs

40 pages

Scientific paper

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.

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