On the regularity criterion of weak solution for the 3D viscous Magneto-hydrodynamics equations

Abstract

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

13pages

References in corpus (2)

• The Beale-Kato-Majda criterion to the 3D Magneto-hydrodynamics equations
• On the regularity of weak solutions of the 3D Navier-Stokes equations in $B_{\infty ,\infty }^{-1}$

Cited by in corpus (19)

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• Global regularity of solutions for the 3D non-resistive and non-diffusive MHD-Boussinesq system with axisymmetric data
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• Regularity criteria for the 3D Navier-Stokes and MHD equations
• A Mixed DG method and an HDG method for incompressible magnetohydrodynamics
• Global well-posedness to the 3D incompressible MHD equations with a new class of large initial data
• Global Regularity of 2D almost resistive MHD Equations
• Two regularity criteria for the 3D MHD equations
• Regularity criteria for the 3D MHD equations in term of velocity
• Application of harmonic analysis techniques to regularity problems of dissipative equations
• An attempt at axiomatization of extending mechanism of solutions to the fluid dynamical systems
• Regularity theory for the dissipative solutions of the MHD equations
• On the partial regularity theory for the MHD equations
• Non blow-up criterion for the 3-D Magneto-hydrodynamics equations in the limiting case
• On the Well-posedness of Magnetohydrodynamics Equations for Incompressible Electrically-Conducting Fluids
• Regularity criteria for suitable weak solutions to the four dimensional incompressible magneto-hydrodynamic equations near boundary
• Local wellposedness for the non-resistive MHD equations in optimal Sobolev spaces