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 γ1,γ2>1, γ1≥n/3, and γ1+γ2≥n in Rn 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.
In: Nonlinear Analysis: Real World Applications, Vol. 38, 01.12.2017, p. 171-183.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 -