Universality of the blow-up profile for small type II blow-up solutions of energy-critical wave equation: the non-radial case

2010/03/02 by Thomas Duyckaerts, Duyckaerts, Thomas, Carlos E. Kenig +4 · 1 citation
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.1003.0625

New version. As notified by Pr. Changxin Miao and Dr. Jiqiang Zheng, a constant was wrong in the statements of Theorem 2 and Lemma 2.6. The statements and proofs were corrected

openalex publication_date 2010/03/02 · arxiv created 2013/11/04 · arxiv updated 2013/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Following our previous paper in the radial case, we consider blow-up type II solutions to the energy-critical focusing wave equation. Let W be the unique radial positive stationary solution of the equation. Up to the symmetries of the equation, under an appropriate smallness assumption, any type II blow-up solution is asymptotically a regular solution plus a rescaled Lorentz transform of W concentrating at the origin.

Citations

• On the formation of singularities in the critical O (3) σ -model
• Personal communication

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• Classification of radial solutions of energy-critical wave systems

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