On the Formation of Singularities in the Critical O(3) Sigma-Model
| dc.creator | Rodnianski, Igor | |
| dc.creator | Sterbenz, Jacob | |
| dc.date | 2006-04-30 | |
| dc.date | 2008-08-22 | |
| dc.date.accessioned | 2026-07-07T09:57:43Z | |
| dc.date.available | 2026-07-07T09:57:43Z | |
| dc.description | We study the phenomena of energy concentration for the critical O(3) sigma model, also known as the wave map flow from R^{2+1} Minkowski space into the sphere S^2. We establish rigorously and constructively existence of a set of smooth initial data resulting in a dynamic finite time formation of singularities. The construction and analysis is done in the context of the k-equivariant symmetry reduction, and we restrict to maps with homotopy class k>3. The concentration mechanism we uncover is essentially due to a resonant self-focusing (shrinking) of a corresponding harmonic map. We show that the phenomenon is generic (e.g. in certain Sobolev spaces) and persists under small perturbations of initial data, while the resulting blowup is bounded by a log-modified self-similar asymptotic. | |
| dc.description | 51 pages added remarks and references corrected computation of the constant in the Appendix A, leading to the stable blow up with the rate bounded from above by a log-modified self-similar asymptotic and from below by a self-similar rate | |
| dc.identifier | https://arxiv.org/abs/math/0605023 | |
| dc.identifier | http://arxiv.org/abs/math/0605023 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/167450 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Mathematical Physics | |
| dc.title | On the Formation of Singularities in the Critical O(3) Sigma-Model | |
| dc.type | text |