| eBook ISBN: | 978-1-4704-0457-4 |
| Product Code: | MEMO/181/853.E |
| List Price: | $60.00 |
| MAA Member Price: | $54.00 |
| AMS Member Price: | $36.00 |
| eBook ISBN: | 978-1-4704-0457-4 |
| Product Code: | MEMO/181/853.E |
| List Price: | $60.00 |
| MAA Member Price: | $54.00 |
| AMS Member Price: | $36.00 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 181; 2006; 80 ppMSC: Primary 35
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.
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Table of Contents
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Chapters
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1. Introduction, controlling spherically symmetric wave maps
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2. Technical preliminaries. Proofs of main theorems
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3. The proof of Proposition 2.2
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4. Proof of Theorem 2.3
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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.
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Chapters
-
1. Introduction, controlling spherically symmetric wave maps
-
2. Technical preliminaries. Proofs of main theorems
-
3. The proof of Proposition 2.2
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4. Proof of Theorem 2.3
