### 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) |
---|---|

Pages (from-to) | 171-183 |

Number of pages | 13 |

Journal | Nonlinear Analysis: Real World Applications |

Volume | 38 |

DOIs | |

State | Published - Dec 1 2017 |

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### 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.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Low Regularity Global Solutions for a generalized MHD-α system

AU - Pennington, Nathan

PY - 2017/12/1

Y1 - 2017/12/1

N2 - 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 γ1,γ2>1, γ1≥n/3, and γ1+γ2≥n in Rn for n≥3.

AB - 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 γ1,γ2>1, γ1≥n/3, and γ1+γ2≥n in Rn for n≥3.

UR - http://www.scopus.com/inward/record.url?scp=85019630144&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85019630144&partnerID=8YFLogxK

U2 - 10.1016/j.nonrwa.2017.04.014

DO - 10.1016/j.nonrwa.2017.04.014

M3 - Article

VL - 38

SP - 171

EP - 183

JO - Nonlinear Analysis: Real World Applications

JF - Nonlinear Analysis: Real World Applications

SN - 1468-1218

ER -