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Regularity Criteria for the Generalized MHD Equations
Abstract
This paper derives regularity criteria for the generalized magnetohydrodynamics (MHD) equations, a system of equations resulting from replacing the Laplacian −Δ in the usual MHD equations by a fractional Laplacian (−Δ)α. These criteria impose assumptions on the velocity field u alone and sharpen a result of He and Xin (20059.
He , C. , Xin , Z. ( 2005 ). On the regularity of weak solutions to the magnetohydrodynamic equations . J. Differential Equations 213 : 235 – 254 .
[CrossRef], [Web of Science ®]
View all references). In addition, these criteria apply to the incompressible Navier–Stokes equations and improve some existing results.
Keywords
2000 Mathematics Subject Classification
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- Available online: 06 Feb 2008
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- a Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma, USA
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