On the three-dimensional magnetohydrodynamics system in scaling-invariant spaces

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We study the criterion for the velocity and magnetic vector fields that solve the three-dimensional magnetohydrodynamics system, given any initial data sufficiently smooth, to experience a finite-time blowup. Following the work of Chemin and Zhang [12] and making use of the structure of the system, we obtain a criterion that is imposed on the magnetic vector field and only one of the three components of the velocity vector field, both in scaling-invariant spaces.

Original languageEnglish
Pages (from-to)575-614
Number of pages40
JournalBulletin des Sciences Mathematiques
Issue number5
StatePublished - Jun 1 2016


  • Anisotropic Littlewood–Paley theory
  • Global regularity
  • Magnetohydrodynamics system
  • Navier–Stokes equations


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