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On the Stability of Self-Similar Solutions to Nonlinear Wave Equations

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Abstract

We consider an explicit self-similar solution to an energy-supercritical Yang-Mills equation and prove its mode stability. Based on earlier work by one of the authors, we obtain a fully rigorous proof of the nonlinear stability of the self-similar blowup profile. This is a large-data result for a supercritical wave equation. Our method is broadly applicable and provides a general approach to stability problems related to self-similar solutions of nonlinear wave equations.

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Authors and Affiliations

  1. Department of Mathematics, The Ohio State University, 231 W 18th Ave, Columbus, OH, 43220, USA

    Ovidiu Costin & Irfan Glogić

  2. Mathematisches Institut, Rheinische Friedrich-Wilhelms-Universität Bonn, Endenicher Allee 60, 53115, Bonn, Germany

    Roland Donninger

  3. Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong

    Min Huang

Authors
  1. Ovidiu Costin
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  2. Roland Donninger
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  3. Irfan Glogić
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  4. Min Huang
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Corresponding author

Correspondence to Ovidiu Costin.

Additional information

Communicated by W. Schlag

Roland Donninger is supported by a Sofja Kovalevskaja Award granted by the Alexander von Humboldt Foundation and the German Federal Ministry of Education and Research.

Ovidiu Costin is partially supported by the NSF DMS Grant 1108794.

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Costin, O., Donninger, R., Glogić, I. et al. On the Stability of Self-Similar Solutions to Nonlinear Wave Equations. Commun. Math. Phys. 343, 299–310 (2016). https://doi.org/10.1007/s00220-016-2588-9

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  • DOI: https://doi.org/10.1007/s00220-016-2588-9

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