Stable self-similar blowup in energy supercritical Yang-Mills theory

Donninger, Roland

In: Mathematische Zeitschrift, 2014, vol. 278, no. 3-4, p. 1005-1032

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    We consider the Cauchy problem for an energy supercritical nonlinear wave equation that arises in $$(1+5)$$ ( 1 + 5 ) -dimensional Yang-Mills theory. A certain self-similar solution $$W_0$$ W 0 of this model is conjectured to act as an attractor for generic large data evolutions. Assuming mode stability of $$W_0$$ W 0 , we prove a weak version of this conjecture, namely that the self-similar solution $$W_0$$ W 0 is (nonlinearly) stable. Phrased differently, we prove that mode stability of $$W_0$$ W 0 implies its nonlinear stability. The fact that this statement is not vacuous follows from careful numerical work by Bizoń and Chmaj that verifies the mode stability of $$W_0$$ W 0 beyond reasonable doubt.