Stability of spherically symmetric wave maps
著者
書誌事項
Stability of spherically symmetric wave maps
（Memoirs of the American Mathematical Society, no. 853）
American Mathematical Society, 2006
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注記
"Volume 181, number 853 (second of 5 numbers)"
Includes bibliographical references (p. 79-80)
内容説明・目次
内容説明
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.
目次
- Introduction, controlling spherically symmetric wave maps Technical preliminaries. Proofs of main theorems The proof of Proposition
- 2.2 Proof of theorem
- 2.3 Bibliography.
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