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Stability of Spherically Symmetric Wave Maps

Joachim Krieger
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Abstract

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+μ}, μ>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+δ}, δ<μ_{0}(μ). 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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Joachim Krieger. 2005-03-02. Stability of Spherically Symmetric Wave Maps. https://arxiv.org/abs/math/0503048

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