2005/08/29 by Joachim Krieger, Wilhelm Schlag, Krieger, Joachim +1 · 1 citation
Mathematics · Physics and Astronomy · #35L05 #35P25 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems #math-ph #math.AP #math.MP #msc:35L05 #msc:35P25
paper · pdf · doi:10.48550/arxiv.math/0508574
In this new version some typos have been fixed
openalex publication_date 2005/08/29 · arxiv created 2005/09/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The focusing critical wave equation in three dimensions exhibits a special class of static solutions which are linearly unstable. These solutions decay like an inverse first power. We construct small codimension one stable manifolds in the class of radial perturbations for these static solutions. We show that initial data on this manifold lead to global solutions. Moreover, the long-time behavior of these solutions can be described explicitly. In particular, the family of static solutions acts as an attractor for these solutions. On a technical level, we remark that the linearized operator exhibits a zero energy resonance, and we develop the tools needed for that case.