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Abstract In this paper, we use the bootstrap argument to prove the uniform-in- k global strong solutions of the 2D density-dependent incompressible magnetic Bénard problem in a bounded domain. Here k is the heat conductivity coefficient. [ABSTRACT FROM AUTHOR]

Abstract In this paper we consider the 3D compressible MHD system in a bounded domain. We first prove a regularity criterion and then use it and the bootstrap argument to show the uniform-in- η global small solutions. Here η is the resistivity coefficient. [ABSTRACT FROM AUTHOR]

Abstract This work establishes a new regularity criterion for the 3D incompressible magneto-hydrodynamical (MHD) equations in terms of one directional derivative of the velocity (i.e., ∂ 3 u) on framework of the anisotropic Lebesgue spaces. More precisely, it is proved that if ∂ 3 u satisfies ∫ 0 T ‖ ‖ ∂ 3 u (τ) ‖ L x 3 α ‖ L x 1 x 2 β q d τ < + ∞ , where 2 q + 1 α + 2 β = k ∈ [ 1 , 3 2 ] and 3 k < α ≤ β ≤ 1 k − 1 , for some T > 0 , then the corresponding solution (u , b) to the 3D MHD equations is regular on (0 , T) × R 3. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we establish a new regularity criterion for the two-dimensional incompressible generalized magnetohydrodynamics equations. [ABSTRACT FROM AUTHOR]

In this paper, we consider the two-dimensional dissipative surface quasi-geostrophic equation, and establish a logarithmically improved regularity criterion. Consequently, our result extends the regularity criterion result of Dong and Pavlovié (2009). In addition, a logarithmically improved regularity criterion to the three-dimensional Navier–Stokes equations is also derived by the same arguments. Therefore, this result extends and improves many previous works. [ABSTRACT FROM AUTHOR]

In this paper, we consider the three-dimensional incompressible Hall–magnetohydrodynamic equations, and establish an improved regularity criterion of local in time classical solutions involving only the vorticity field. Consequently, this improves the previous result. [ABSTRACT FROM AUTHOR]

In this short paper, we consider the two-dimensional inviscid Boussinesq equations and establish an improved regularity criterion. [ABSTRACT FROM AUTHOR]

This paper proves a regularity criterion for 3D density-dependent incompressible magnetohydrodynamic flows with density-dependent viscosity coefficient. In particular, we build a blowup criterion just in terms of the gradient of density and velocity, and the initial density need not be strictly positive. [ABSTRACT FROM AUTHOR]

This paper proves a regularity criterion for a 3D generalized Hall-MHD system in terms of velocity gradient in negative Besov spaces. [ABSTRACT FROM AUTHOR]

This paper concerns with the regularity criteria for the 3 D axisymmetric MHD system. It is proved that the control of swirl component of vorticity can ensure the smoothness of the solution. [ABSTRACT FROM AUTHOR]

This paper proves some regularity criteria for the 3D (density-dependent) incompressible Maxwell–Navier–Stokes system, which improves a recent result of Kang and Lee (2013). [ABSTRACT FROM AUTHOR]

This paper proves a regularity criterion ∇ u , ∇ b ∈ L ∞ ( 0 , T ; L ∞ ) for 3D ideal density-dependent MHD system. [ABSTRACT FROM AUTHOR]

This paper proves some regularity criteria for some simplified non-isothermal models for nematic liquid crystals. [ABSTRACT FROM AUTHOR]

In this paper, we consider the two-dimensional (2D) Boussinesq equations with partial dissipation. The issue of whether the 2D Boussinesq equations always possess global (in time) classical solutions can be difficult when there is only partial dissipation. Therefore, the goal of this paper is to establish some regularity criteria of the corresponding systems. [ABSTRACT FROM AUTHOR]

In this paper we establish the regularity criteria of solutions to the three space dimensions generalized viscous Hall-magnetohydrodynamics. Moreover, we also prove that there exist classical solutions globally in time to the generalized viscous Hall-MHD if the initial data is small enough or the fractional Laplacian dissipation powers α and β are suitably large. These results are some improvements of very recent work (Chae and Lee, 2014) established by Chae and Lee. [ABSTRACT FROM AUTHOR]

Abstract: In this work, we study the regularity criterion of the three-dimensional nematic liquid crystal flows. It is proved that if the vorticity satisfies where denotes the critical Besov space, then the solution becomes a regular solution on . This result extends the recent regularity criterion obtained by Fan and Ozawa (2012) [11]. [Copyright &y& Elsevier]