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Nonexistence of self-similar singularities in the viscous magnetohydrodynamics with zero resistivity

Authors :
Chae, Dongho
Source :
Journal of Functional Analysis. Jan2008, Vol. 254 Issue 2, p441-453. 13p.
Publication Year :
2008

Abstract

Abstract: We are concerned on the possibility of finite time singularity in a partially viscous magnetohydrodynamic equations in , , 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 . 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. [Copyright &y& Elsevier]

Details

Language :
English
ISSN :
00221236
Volume :
254
Issue :
2
Database :
Academic Search Index
Journal :
Journal of Functional Analysis
Publication Type :
Academic Journal
Accession number :
27901340
Full Text :
https://doi.org/10.1016/j.jfa.2007.10.001