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

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arxiv 1405.0082 v1 pith:3PQ3AE7C submitted 2014-05-01 math.AP

Xianpeng Hu , Fanghua Lin This is my paper · ORCID
classification math.AP
keywords magneticdiffusivityexistenceflowsincompressiblemagnetohydrodynamiczerobackground
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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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Nonlinear stability of a background magnetic field for the 3D compressible MHD equations with anisotropic dissipation

    math.AP 2026-07 conditional novelty 7.0 of 10

    Global nonlinear stability is proved for 3D compressible MHD near a background magnetic field with only horizontal velocity dissipation and one-directional magnetic diffusion.

  2. Families of curves in Vinberg representations

    math.NT 2025-08 unverdicted novelty 7.0 of 10

    Families of curves associated to nilpotents in Z/mZ-graded Lie algebras are classified, and the 5-Selmer orbit parametrization over Q follows from an E8 grading.

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