Low Regularity Global Solutions for a generalized MHD-α system

Research output: Contribution to journalArticle

Abstract

The Magneto-Hydrodynamic (MHD) system of equations governs the motion of viscous fluids subject to a magnetic field. Due to the difficulty of obtaining global solutions to the MHD system, it has become common to study modified versions of the system. In this paper, we prove the existence of a unique global solution to the incompressible MHD-α system with diffusion terms which are Fourier multipliers with symbols of the form m(ξ)=|ξ|γ/g(|ξ|) for γ>0 and g (essentially) a logarithm. Letting γ1 and γ2 be the regularity of the diffusion terms, we obtain global existence when γ1 and γ2 satisfy γ12>1, γ1≥n/3, and γ12≥n in Rn for n≥3.

Original languageEnglish (US)
Pages (from-to)171-183
Number of pages13
JournalNonlinear Analysis: Real World Applications
Volume38
DOIs
StatePublished - Dec 1 2017

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Hydrodynamics
Global Solution
Regularity
Fourier multipliers
Magnetic Fields
Term
Viscous Fluid
Logarithm
Global Existence
System of equations
Magnetic Field
Magnetic fields
Fluids
Motion

All Science Journal Classification (ASJC) codes

  • Analysis
  • Medicine(all)
  • Engineering(all)
  • Economics, Econometrics and Finance(all)
  • Computational Mathematics
  • Applied Mathematics

Cite this

Low Regularity Global Solutions for a generalized MHD-α system. / Pennington, Nathan.

In: Nonlinear Analysis: Real World Applications, Vol. 38, 01.12.2017, p. 171-183.

Research output: Contribution to journalArticle

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