Regularity criteria of the three-dimensional MHD system involving one velocity and one vorticity component

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Abstract

We obtain a regularity criteria of the solution to the three-dimensional magnetohydrodynamics system to remain smooth for all time involving only one velocity and one vorticity component. Moreover, the norm in space and time with which we impose our criteria for the vorticity component is at the scaling invariant level. The proof requires a new decomposition of the four non-linear terms making use of a new identity due to the divergence-free conditions of the velocity and the magnetic vector fields.

Original languageEnglish
Pages (from-to)73-83
Number of pages11
JournalNonlinear Analysis, Theory, Methods and Applications
Volume135
DOIs
StatePublished - Apr 1 2016

Keywords

  • 35Q35
  • 35Q86
  • MSC 35B65

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