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.


35L05 Wave equation
35L70 Second-order nonlinear hyperbolic equations
Full Text: DOI arXiv Link