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.

On regularity criteria of a weak solution to the three-dimensional magnetohydrodynamics equations in Lorentz space

2018 ◽  
Vol 148 (3) ◽  
pp. 593-604
Author(s):  
Jae-Myoung Kim
Keyword(s):  
Weak Solution ◽  
Bounded Domain ◽  
Lorentz Space ◽  
Three Dimensional ◽  
Regularity Criterion ◽  
Regularity Criteria ◽  
Magnetohydrodynamics Equations

We give a weak-Lp Serrin-type regularity criterion for a weak solution to the three-dimensional magnetohydrodynamics equations in a bounded domain Ω ⊂ ℝ3.

A LOGARITHMALLY IMPROVED BLOW-UP CRITERION OF SMOOTH SOLUTIONS FOR THE THREE-DIMENSIONAL MHD EQUATIONS

2012 ◽  
Vol 23 (02) ◽  
pp. 1250027 ◽  
Author(s):  
YU-ZHU WANG ◽  
HENGJUN ZHAO ◽  
YIN-XIA WANG
Keyword(s):  
Cauchy Problem ◽  
Blow Up ◽  
Three Dimensional ◽  
Mhd Equations ◽  
Magnetohydrodynamic Equations ◽  
Smooth Solutions ◽  
The Cauchy Problem ◽  
Incompressible Magnetohydrodynamic Equations ◽  
Blow Up Criterion

In this paper we investigate the Cauchy problem for the three-dimensional incompressible magnetohydrodynamic equations. A logarithmal improved blow-up criterion of smooth solutions is obtained.

scholarly journals Remarks on the Regularity Criterion of the Navier-Stokes Equations with Nonlinear Damping

2015 ◽  
Vol 2015 ◽  
pp. 1-5
Author(s):  
Weihua Wang ◽  
Guopeng Zhou
Keyword(s):  
Weak Solution ◽  
Weak Solutions ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Regularity Criterion ◽  
Nonlinear Damping ◽  
Navier Stokes ◽  
Navier Stokes Equations

This paper is concerned with the regularity criterion of weak solutions to the three-dimensional Navier-Stokes equations with nonlinear damping in critical weakLqspaces. It is proved that if the weak solution satisfies∫0T∇u1Lq,∞2q/2q-3+∇u2Lq,∞2q/2q-3/1+ln⁡e+∇uL22ds<∞,  q>3/2, then the weak solution of Navier-Stokes equations with nonlinear damping is regular on(0,T].

scholarly journals THE ARTIFICIAL COMPRESSIBILITY APPROXIMATION FOR MHD EQUATIONS IN UNBOUNDED DOMAIN

2013 ◽  
Vol 10 (01) ◽  
pp. 181-198 ◽  
Author(s):  
DONATELLA DONATELLI
Keyword(s):  
Wave Equation ◽  
Weak Solution ◽  
Unbounded Domains ◽  
Mhd Equations ◽  
Magnetohydrodynamic Equations ◽  
Artificial Compressibility ◽  
Dispersive Estimate ◽  
Artificial Compressibility Method ◽  
Mhd System ◽  
Incompressible Magnetohydrodynamic Equations

We analyze a method of approximation for the weak solutions of the incompressible magnetohydrodynamic equations (MHD) in unbounded domains. In particular we describe an hyperbolic version of the so-called artificial compressibility method adapted to the MHD system. By exploiting the wave equation structure of the approximating system we achieve the convergence of the approximating sequences by means of dispersive estimate of Strichartz type. We prove that the soleinoidal component of the approximating velocity and magnetic fields is relatively compact and converges strongly to a weak solution of the MHD equation.

scholarly journals Logarithmical Regularity Criteria of the Three-Dimensional Micropolar Fluid Equations in terms of the Pressure

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Yan Jia ◽  
Jing Zhang ◽  
Bo-Qing Dong
Keyword(s):  
Partial Derivative ◽  
Besov Spaces ◽  
Micropolar Fluid ◽  
Three Dimensional ◽  
Regularity Criterion ◽  
Regularity Criteria ◽  
Lebesgue Spaces ◽  
Fluid Equations ◽  
Micropolar Fluid Equations

This paper is devoted to the regularity criterion of the three-dimensional micropolar fluid equations. Some new regularity criteria in terms of the partial derivative of the pressure in the Lebesgue spaces and the Besov spaces are obtained which improve the previous results on the micropolar fluid equations.

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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