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arxiv: 1405.0082 · v1 · submitted 2014-05-01 · 🧮 math.AP

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

Xianpeng Hu , Fanghua Lin
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classification 🧮 math.AP
keywords magneticdiffusivityexistenceflowsincompressiblemagnetohydrodynamiczerobackground
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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.

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Cited by 2 Pith papers

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    Establishes global uniform regularity and vanishing dissipation limits for 3D compressible MHD near a background magnetic field via a two-tier energy method.

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    The authors prove global uniform regularity and vanishing dissipation limits for anisotropic 3D compressible MHD equations near a background magnetic field via a two-tier energy method.