Equivariant wave maps exterior to a ball

Details Equivariant wave maps exterior to a ball Equivariant wave maps exterior to a ball

2011-10-21

arxiv.org/abs/1110.4762v1

Physics

Mathematical Physics

16 pages, 9 figures

Scientific paper

We consider the exterior Cauchy-Dirichlet problem for equivariant wave maps from 3+1 dimensional Minkowski spacetime into the three-sphere. Using mixed analytical and numerical methods we show that, for a given topological degree of the map, all solutions starting from smooth finite energy initial data converge to the unique static solution (harmonic map). The asymptotics of this relaxation process is described in detail. We hope that our model will provide an attractive mathematical setting for gaining insight into dissipation-by-dispersion phenomena, in particular the soliton resolution conjecture.

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