Global Existence for Two Dimensional Incompressible Magnetohydrodynamic Flows with Zero Magnetic Diffusivity
Abstract
The existence of globalintime classical solutions to the Cauchy problem of incompressible Magnetohydrodynamic flows with zero magnetic diffusivity is considered in two dimensions. The linearization of equations is a degenerated parabolichyperbolic system. The solution is constructed as a small perturbation of a constant background in critical spaces. The deformation gradient has been introduced to decouple the subtle coupling between the flow and the magnetic field. The $L^1$ dissipation of the velocity is obtained.
 Publication:

arXiv eprints
 Pub Date:
 April 2014
 arXiv:
 arXiv:1405.0082
 Bibcode:
 2014arXiv1405.0082H
 Keywords:

 Mathematics  Analysis of PDEs