Global regularity of logarithmically supercritical 3-D LAMHD-alpha system with zero diffusion

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Abstract

We study the three-dimensional Lagrangian-averaged magnetohydrodynamics-alpha system with zero diffusion. Despite the dissipation strength at the logarithmically supercritical level, using dyadic decomposition techniques we show that given initial data sufficiently smooth, the solution pair remains smooth for all time. This settles the global regularity case suggested by the authors in [27].

Original languageEnglish
Pages (from-to)835-846
Number of pages12
JournalJournal of Mathematical Analysis and Applications
Volume436
Issue number2
DOIs
StatePublished - Apr 15 2016

Keywords

  • Besov spaces
  • Criticality
  • Global regularity
  • Magnetohydrodynamics system
  • Navier-Stokes equations

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