Regularity results on the Leray-alpha magnetohydrodynamics systems

Durga Kc, Kazuo Yamazaki

Research output: Contribution to journalArticle

6 Scopus citations

Abstract

We study certain generalized Leray-alpha magnetohydrodynamics systems. We show that the solution pairs of velocity and magnetic fields to this system in two-dimension preserve their initial regularity in two cases: dissipation logarithmically weaker than a full Laplacian and zero diffusion, zero dissipation and diffusion logarithmically weaker than a full Laplacian. These results extend previous results in Zhou and Fan (2011). Moreover, we show that for a certain three-dimensional Leray-alpha magnetohydrodynamics system, sufficient condition of regularity may be reduced to a horizontal gradient or a partial derivative in just one direction of the magnetic field, reducing components from the results in Fan and Ozawa (2009).

Original languageEnglish
Pages (from-to)178-197
Number of pages20
JournalNonlinear Analysis: Real World Applications
Volume32
DOIs
StatePublished - Dec 1 2016

Keywords

  • Besov spaces
  • Magnetohydrodynamics system
  • Navier-Stokes equations
  • Regularity

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