On the Regularity Criterion of Weak Solution for the 3D Viscous Magneto-Hydrodynamics Equations

By Qionglei Chen, Changxing Miao, Zhifei Zhang. 2007

219 citations recorded by the source corpus.

We improve and extend some known regularity criterion of the weak solution for the 3D viscous Magneto-hydrodynamics equations by means of the Fourier localization technique and Bony’s para-product decomposition.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/04db310b1157720587ebe81faf501a2dbe64f35c

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In Applied Mathematics

In Control and Systems Engineering

In Mathematical Physics

Citations in the corpus

Regularity criteria for the solutions to the 3D MHD equations in the multiplier space (2010, result): “After finished this work, we were informed that the result in [ 2 ] covered our first one in terms of”
Global Regularity for a Class of Generalized Magnetohydrodynamic Equations (2011, unknown): “, [3,4,8–11,13–15,17,20–23,25]).”
On axially symmetric incompressible magnetohydrodynamics in three dimensions (2012, background): “We also emphasis the partial regularity theory and Serrin type criterions in [6, 7], and various blowup criterions in [1, 4] (see also the reference therein).”
Logarithmically improved regularity criterion for the Boussinesq equations in Besov spaces with negative indices (2016, methodology): “[9] (see also [4,29,30]) refined the following blow-up criterion by applying Bony paraproduct decomposition to both the momentum equations and the diffusive equation (refer to the similar argument by Chen, Miao and Zhang [31] for MHD”