Nonexistence of self-similar singularities in the ideal magnetohydrodynamics
| dc.creator | Chae, Dongho | |
| dc.date | 2007-03-12 | |
| dc.date | 2007-04-09 | |
| dc.date.accessioned | 2026-07-07T07:55:38Z | |
| dc.date.available | 2026-07-07T07:55:38Z | |
| dc.description | In this paper we exclude the scenario of apparition of finite time singularity in the form of self-similar singularities in the ideal magnetohydrodynamic equations, assuming suitable integrability conditions on the vorticity and the magnetic field. We also consider more sophisticated possibility of asymptotically self-similar singularities, which means that the local classical solution converges to the self-similar profile as we approaches to the possible time of singularity. The scenario of asymptotically self-similar singularity is also excluded under suitable conditions on the profile. In the 2D magnetohydrodynamics the magnetic field evolution equations reduce to a divergence free transport equation for a scalar stream function. This helps us to improve the above nonexistence theorems on the self-similar singularities, in the sense that we only need weaker integrability conditions on the profile to prove the results. | |
| dc.description | 23 pages | |
| dc.identifier | https://arxiv.org/abs/math/0703317 | |
| dc.identifier | http://arxiv.org/abs/math/0703317 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/127034 | |
| dc.subject | Analysis of PDEs | |
| dc.title | Nonexistence of self-similar singularities in the ideal magnetohydrodynamics | |
| dc.type | text |