Communications in Mathematical Physics

, Volume 343, Issue 1, pp 299–310 | Cite as

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

  • Ovidiu Costin
  • Roland Donninger
  • Irfan Glogić
  • Min Huang
Article

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Ovidiu Costin
    • 1
  • Roland Donninger
    • 2
  • Irfan Glogić
    • 1
  • Min Huang
    • 3
  1. 1.Department of MathematicsThe Ohio State UniversityColumbusUSA
  2. 2.Mathematisches InstitutRheinische Friedrich-Wilhelms-Universität BonnBonnGermany
  3. 3.Department of MathematicsCity University of Hong KongKowloonHong Kong

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