Stability of spherically symmetric wave maps
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\les…
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- Full title :Stability of spherically symmetric wave maps / Joachim Krieger.
Summary
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 $H {1+\delta}, \delta\less\mu_{0}$ 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.
Read More ↓Edition Statements
- Publication Date:2006.
Publication Statements
- Publisher(s):American mathematical Society
- Place of Publication:Providence, R.I
- Language:eng
- Publication Date:2006.
Notes
"Volume 181, number 853 (second of 5 numbers)."
The Physical Object
- Description:vii, 80 pages ; : 26 cm.
Edition Identifiers
- ISBN:0821838776, 9780821838778
- oclc:ocm63108466
- LC Classification:QA3
- Dewey Decimal:510 s
Table of Contents
1. Introduction, controlling spherically symmetric wave maps -- 2. Technical preliminaries. Proofs of main theorems -- 3. The proof of Proposition 2.2 -- 4. Proof of theorem 2.3.
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