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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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