**Memoirs of the American Mathematical Society**

2006;
80 pp;
Softcover

MSC: Primary 35;

Print ISBN: 978-0-8218-3877-8

Product Code: MEMO/181/853

List Price: $60.00

AMS Member Price: $36.00

MAA member Price: $54.00

**Electronic ISBN: 978-1-4704-0457-4
Product Code: MEMO/181/853.E**

List Price: $60.00

AMS Member Price: $36.00

MAA member Price: $54.00

# Stability of Spherically Symmetric Wave Maps

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*Joachim Krieger*

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