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Mathematics > Analysis of PDEs

arXiv:1405.0082 (math)
[Submitted on 1 May 2014]

Title:Global Existence for Two Dimensional Incompressible Magnetohydrodynamic Flows with Zero Magnetic Diffusivity

Authors:Xianpeng Hu, Fanghua Lin
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Abstract:The existence of global-in-time 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 parabolic-hyperbolic 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.
Subjects: Analysis of PDEs (math.AP)
Cite as: arXiv:1405.0082 [math.AP]
  (or arXiv:1405.0082v1 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1405.0082

Submission history

From: Xianpeng Hu [view email]
[v1] Thu, 1 May 2014 03:10:07 UTC (17 KB)
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