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15 February 2020 On the stability of blowup solutions for the critical corotational wave-map problem
Joachim Krieger, Shuang Miao
Duke Math. J. 169(3): 435-532 (15 February 2020). DOI: 10.1215/00127094-2019-0053

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 λ(t)=t1ν is sufficiently close to t1; that is, the constant ν 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

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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

Received: 14 March 2018; Revised: 7 July 2019; Published: 15 February 2020
First available in Project Euclid: 8 January 2020

zbMATH: 07198459
MathSciNet: MR4065147
Digital Object Identifier: 10.1215/00127094-2019-0053

Subjects:
Primary: 35L05
Secondary: 35B40

Rights: Copyright © 2020 Duke University Press

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Vol.169 • No. 3 • 15 February 2020
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