A new regularity criterion for weak solutions to the viscous MHD equations in terms of the vorticity field

2010 ◽  
Vol 72 (9-10) ◽  
pp. 3643-3648 ◽  
Author(s):  
Yong Zhou ◽  
Sadek Gala
Keyword(s):  
Weak Solutions ◽  
Regularity Criterion ◽  
Mhd Equations ◽  
Vorticity Field

scholarly journals Logarithmically Improved Regularity Criterion for the 3D Micropolar Fluid Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Hui Zhang
Keyword(s):  
Besov Space ◽  
Strong Solution ◽  
Weak Solutions ◽  
Micropolar Fluid ◽  
Regularity Criterion ◽  
Vorticity Field ◽  
Regularity Of Weak Solutions ◽  
Fluid Equations ◽  
Incompressible Micropolar Fluid ◽  
Micropolar Fluid Equations

We study the regularity of weak solutions to the incompressible micropolar fluid equations. We obtain an improved regularity criterion in terms of vorticity of velocity in Besov space. It is proved that if the vorticity field satisfies ∫0T∇×uB˙∞,∞0/1+log1+∇×uB˙∞,∞0dt<∞ then the strong solution can be smoothly extended after time T.

scholarly journals A Regularity Criterion for the 3D Incompressible Magnetohydrodynamics Equations in the Multiplier Spaces

2017 ◽  
Vol 2017 ◽  
pp. 1-5 ◽  
Author(s):  
Chunhong Tian
Keyword(s):  
Weak Solutions ◽  
Regularity Criterion ◽  
Mhd Equations ◽  
Magnetohydrodynamics Equations ◽  
Partial Derivatives ◽  
Magnetic Components ◽  
Incompressible Mhd ◽  
Derivatives Of ◽  
Incompressible Magnetohydrodynamics

We are concerned with the regularity criterion for weak solutions to the 3D incompressible MHD equations in this paper. We show that if some partial derivatives of the velocity components and magnetic components belong to the multiplier spaces, then the solution actually is smooth on (0,T).

scholarly journals A New Regularity Criterion for the Three-Dimensional Incompressible Magnetohydrodynamic Equations in the Besov Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
TianLi LI ◽  
Wen Wang ◽  
Lei Liu
Keyword(s):  
Weak Solution ◽  
Weak Solutions ◽  
Besov Spaces ◽  
Pressure Field ◽  
Three Dimensional ◽  
Regularity Criterion ◽  
Mhd Equations ◽  
Regularity Criteria ◽  
Magnetohydrodynamic Equations ◽  
Incompressible Magnetohydrodynamic Equations

Regularity criteria of the weak solutions to the three-dimensional (3D) incompressible magnetohydrodynamic (MHD) equations are discussed. Our results imply that the scalar pressure field π plays an important role in the regularity problem of MHD equations. We derive that the weak solution u , b is regular on 0 , T , which is provided for the scalar pressure field π in the Besov spaces.

scholarly journals Regularity Criteria for the 3D Magneto-Hydrodynamics Equations in Anisotropic Lorentz Spaces

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 625
Author(s):  
Maria Alessandra Ragusa ◽  
Fan Wu
Keyword(s):  
Weak Solutions ◽  
Lorentz Space ◽  
Regularity Criterion ◽  
Lorentz Spaces ◽  
Mhd Equations ◽  
Regularity Criteria ◽  
Regularity Of Weak Solutions ◽  
Incompressible Mhd ◽  
Hydrodynamics Equations

In this paper, we investigate the regularity of weak solutions to the 3D incompressible MHD equations. We provide a regularity criterion for weak solutions involving any two groups functions (∂1u1,∂1b1), (∂2u2,∂2b2) and (∂3u3,∂3b3) in anisotropic Lorentz space.

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