## Stability of spherically symmetric wave maps.(English)Zbl 1387.35392

Mem. Am. Math. Soc. 853, 80 p. (2006).
Summary (arXiv): We study wave maps from $$\mathbb R^{2+1}$$ to the hyperbolic plane with smooth compactly supported initial data which are close to smooth spherically symmetric ones with respect to some $$H^{1+\mu},~\mu>0$$. We show that such wave maps don’t develop singularities and stay close to the wave pap extending the spherically symmetric data with respect to all $$H^{1+\delta},~\delta<\mu_{0}(\mu)$$. We obtain a similar result for wave maps whose initial data are close to geodesic ones. This generalizes a theorem of Sideris for this context.

### MSC:

 35L05 Wave equation 35L70 Second-order nonlinear hyperbolic equations
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