Nonexistence of self-similar singularities in the viscous magnetohydrodynamics with zero resistivity
| dc.creator | Chae, Dongho | |
| dc.date | 2007-03-28 | |
| dc.date | 2007-05-02 | |
| dc.date.accessioned | 2026-07-07T07:59:00Z | |
| dc.date.available | 2026-07-07T07:59:00Z | |
| dc.description | We are concerned on the possibility of finite time singularity in a partially viscous magnetohydrodynamic equations in $\Bbb R^n$, $n=2,3$, namely the MHD with positive viscosity and zero resistivity. In the special case of zero magnetic field the system reduces to the Navier-Stokes equations in $\Bbb R^n$. In this paper we exclude the scenario of finite time singularity in the form of self-similarity, under suitable integrability conditions on the velocity and the magnetic field. We also prove the nonexistence of asymptotically self-similar singularity. This provides us information on the behavior of solutions near possible singularity of general type as described in Corollary 1.1 below. | |
| dc.description | 16 pages | |
| dc.identifier | https://arxiv.org/abs/math/0703830 | |
| dc.identifier | http://arxiv.org/abs/math/0703830 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/128213 | |
| dc.subject | Analysis of PDEs | |
| dc.title | Nonexistence of self-similar singularities in the viscous magnetohydrodynamics with zero resistivity | |
| dc.type | text |