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


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.


Spectral Problem Unstable Mode Nonlinear Wave Equation Global Regularity Unstable Eigenvalue 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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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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