Abstract
We show that the finite time blowup solutions for the corotational wave-map problem constructed by the first author along with Gao, Schlag, and Tataru are stable under suitably small perturbations within the corotational class, provided that the scaling parameter is sufficiently close to ; that is, the constant is sufficiently small and positive. The method of proof is inspired by recent work by the first author and Burzio, but takes advantage of geometric structures of the wave-map problem, already used in previous work by the first author, Bejenaru, Tataru, Raphaël, and Rodnianski, to simplify the analysis. In particular, we heavily exploit the fact that the resonance at zero satisfies a natural first-order differential equation.
Citation
Joachim Krieger. Shuang Miao. "On the stability of blowup solutions for the critical corotational wave-map problem." Duke Math. J. 169 (3) 435 - 532, 15 February 2020. https://doi.org/10.1215/00127094-2019-0053
Information