Generic self-similar blowup for equivariant wave maps and Yang-Mills fields in higher dimensions

Abstract

We consider equivariant wave maps from the $(d+1)$--dimensional Minkowski spacetime into the $d$-sphere for $d\ge 4$. We find a new explicit stable self-similar solution and give numerical evidence that it plays the role of a universal attractor for generic blowup. An analogous result is obtained for the $SO(d)$ symmetric Yang-Mills field for $d\ge 6$.

9 pages, 2 figures

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Cited by in corpus (10)

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• Mode stability of self-similar wave maps in higher dimensions
• Mathematical General Relativity
• Threshold for blowup for equivariant wave maps in higher dimensions
• Threshold for blowup for the supercritical cubic wave equation
• On the existence and stability of blowup for wave maps into a negatively curved target
• A globally stable self-similar blowup profile in energy supercritical Yang-Mills theory
• Optimal blowup stability for three-dimensional wave maps
• Sharp universal rate for stable blow-up of corotational wave maps
• Nonlinear stability of explicit self-similar solutions for the timelike extremal hypersurfaces in R^{1+3}