On global regularity of 2D generalized magnetohydrodynamic equations

Chuong Van Tran, Xinwei Yu, Zhichun Zhai

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94 Citations (Scopus)
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Abstract

In this article we study the global regularity of 2D generalized magnetohydrodynamic equations (2D GMHD), in which the dissipation terms are –ν(–Δ)αu and –κ(–Δ)βb. We show that smooth solutions are global in the following three cases: α≥1/2, β≥1; 0≤α≤1/2, 2α+β>2; α≥2, β=0. We also show that in the inviscid case ν=0, if β>1, then smooth solutions are global as long as the direction of the magnetic field remains smooth enough.

Original languageEnglish
Pages (from-to)4194-4216
Number of pages23
JournalJournal of Differential Equations
Volume254
Issue number10
Early online date28 Feb 2013
DOIs
Publication statusPublished - 15 May 2013

Keywords

  • Magnetohydrodynamics
  • Global regularity
  • Generalized diffusion

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