Remarks on the global regularity of the two-dimensional magnetohydrodynamics system with zero dissipation

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Abstract

We study the two-dimensional magnetohydrodynamics system with generalized dissipation and diffusion in terms of fractional Laplacians. It is known that the classical magnetohydrodynamics system with full Laplacians in both dissipation and diffusion terms admits a unique global strong solution pair. Making use of the special structure of the system in the two-dimensional case, we show in particular that the solution pair remains smooth when we have zero dissipation but only magnetic diffusion with its power of the fractional Laplacian β>32.

Original languageEnglish
Pages (from-to)194-205
Number of pages12
JournalNonlinear Analysis, Theory, Methods and Applications
Volume94
DOIs
StatePublished - 2014

Keywords

  • Euler equations
  • Global regularity
  • Littlewood-Paley theory
  • Magnetohydrodynamics system
  • Navier-Stokes system

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