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

Abstract

We consider the Cauchy problem for an energy supercritical nonlinear wave equation that arises in $(1+5)$--dimensional Yang--Mills theory. A certain self--similar solution $W_0$ of this model is conjectured to act as an attractor for generic large data evolutions. Assuming mode stability of $W_0$, we prove a weak version of this conjecture, namely that the self--similar solution $W_0$ is (nonlinearly) stable. Phrased differently, we prove that mode stability of $W_0$ 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 $W_0$ beyond reasonable doubt.

References in corpus (3)

• Scattering below critical energy for the radial 4D Yang-Mills equation and for the 2D corotational wave map system
• Stable blow up dynamics for the critical co-rotational Wave Maps and equivariant Yang-Mills problems
• Global Regularity for the Yang-Mills Equations on High Dimensional Minkowski Space

Cited by in corpus (2)

• Nondispersive decay for the cubic wave equation
• Stable blow up dynamics for energy supercritical wave equations