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arXiv · 1803.02706

On stability of blow up solutions for the critical co-rotational Wave Maps problem

Joachim Krieger·Shuang Miao
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Abstract

We show that the finite time blow up solutions for the co-rotational Wave Maps problem constructed in [7,15] are stable under suitably small perturbations within the co-rotational class, provided the scaling parameter $\lambda(t) = t^{-1-\nu}$ is sufficiently close to $t^{-1}$, i. e. the constant $\nu$ is sufficiently small and positive. The method of proof is inspired by [3,12], but takes advantage of geometric structures of the Wave Maps problem already used in [1,21] to simplify the analysis. In particular, we heavily exploit that the resonance at zero satisfies a natural first order differential equation.

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Joachim Krieger, Shuang Miao. 2018-03-07. On stability of blow up solutions for the critical co-rotational Wave Maps problem. https://doi.org/10.1215/00127094-2019-0053

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