Self-similar blowup from arbitrary data for supercritical wave maps with additive noise

2025/10/29 by Glogić, Irfan, Hofmanová, Martina, Luongo, Eliseo
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.2510.25326

Abstract

We consider stochastically perturbed wave maps from ℝ^1+d into \mathbbS^d, in all energy-supercritical dimensions d ≥ 3. We show that corotational non-degenerate Gaussian additive noise leads to self-similar blowup with positive probability for any corotational initial data. The same result without noise is conjectured, but unknown, for large data.

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Related

• Globally stable blowup profile for supercritical wave maps in all dimensions
• On blowup of co-rotational wave maps in odd space dimensions
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• Stable blowup for supercritical wave maps into perturbed spheres
• On stability of self-similar blowup for mass supercritical NLS