Stability of Spherically Symmetric Wave Maps

Details Stability of Spherically Symmetric Wave Maps Stability of Spherically Symmetric Wave Maps

2005-03-02

arxiv.org/abs/math/0503048v1

Mathematics

Analysis of PDEs

78 pages

Scientific paper

We study Wave Maps from R^{2+1} to the hyperbolic plane with smooth compactly supported initial data which are close to smooth spherically symmetric ones with respect to some H^{1+\mu}, \mu>0. We show that such Wave Maps don't develop singularities and stay close to the Wave Map extending the spherically symmetric data with respect to all H^{1+\delta}, \delta<\mu_{0}(\mu). We obtain a similar result for Wave Maps whose initial data are close to geodesic ones. This generalizes a theorem of Sideris for this context.

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