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Stability of Spherically Symmetric Wave Maps

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Stability of Spherically Symmetric Wave Maps Synopsis

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.

About This Edition

ISBN: 9780821838778
Publication date:
Author: Joachim Krieger
Publisher: American Mathematical Society
Format: Paperback
Pagination: 80 pages
Series: Memoirs of the American Mathematical Society
Genres: Calculus and mathematical analysis
Mathematics