Regularity Criteria for the Generalized MHD Equations

By Jiahong Wu. 2008

231 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/dc0eee452f684184131494a11d3e9806319896ea

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Global Regularity for a Class of Generalized Magnetohydrodynamic Equations (2011, unknown): “, [3,4,8–11,13–15,17,20–23,25]).”
Two regularity criteria for the 3D MHD equations (2009, result): “This assumption was weakened in [51] with L-norm replaced by norms in Besov spaces and further improved by Chen, Miao and Zhang in [17].”
Global well posedness for the Maxwell-Navier-Stokes system in 2D (2010, background): “Moreover, most of the mathematical works dealing with existence, uniqueness [13,30,1,2], blow-up criterion [6,20], regularity criteria [15,33,32], long time behavior or inviscid and non-resistive limits [12] or related problems [22] also make this assumption and hence remove the displacement current”
The Beale-Kato-Majda Criterion for the 3D Magneto-Hydrodynamics Equations (2007, methodology): “mentioned conditions. Hence, this also improves the results of [10, 11]. For the further explanation of (1.8), it can be referred to the remarks after Theorem 1 in [15]. Remark 1.2. Very recently, Wu [23] use the energy estimate combined with the Bony paraproduct technique to derive many interesting”
Regularity criteria for the solutions to the 3D MHD equations in the multiplier space (2010, background): “Part of them are listed here: Chen et al. [1] proved regularity by adding condition on ∆j( ∇× u); He and Wang [3] extended it to the weak-L p space L p,∞ ;W ang [9] proved regularity for u ∈ L 2 (0 ,T , BM O); Wu [ 10 ] considered the velocity field being in the homogeneous Besov space; regularity w”
Remarks on global regularity of 2D generalized MHD equations (2013, background): “So the GMHD equations has attracted much interest of many mathematicians and has motivated a large number of research papers concerning various generalizations and improvements [8, 9, 10, 11, 13, 14].”