## 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 γ_{1} and γ_{2} be the regularity of the diffusion terms, we obtain global existence when γ_{1} and γ_{2} satisfy γ_{1},γ_{2}>1, γ_{1}≥n/3, and γ_{1}+γ_{2}≥n in R^{n} for n≥3.

Original language | English (US) |
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Pages (from-to) | 171-183 |

Number of pages | 13 |

Journal | Nonlinear Analysis: Real World Applications |

Volume | 38 |

DOIs | |

State | Published - Dec 1 2017 |

## All Science Journal Classification (ASJC) codes

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