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Abstract This paper proves a regularity criterion for a new density-dependent incompressible Hall-MHD system with positive density. [ABSTRACT FROM AUTHOR]

We prove a regularity criterion for the wave map in a bounded domain when the space dimension n = 2 or 3 . We also prove the global well-posedness of strong solutions for the wave map in a bounded domain when the space dimension n = 1 . [ABSTRACT FROM AUTHOR]

This paper proves a new regularity criterion for a 3D density-dependent incompressible liquid crystals model with positive initial density. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the case of Prodi–Serrin type regularity criterion involving u 3 and ∂ 3 u h . More precisely, it is shown that Leray’s weak solutions of the three-dimensional Navier–Stokes equations become regular if the third component of velocity (or the gradient of the velocity field) satisfies the additional end-point Prodi–Serrin type condition. [ABSTRACT FROM AUTHOR]

We prove a new scaling invariant regularity criterion for the 3D MHD equations via horizontal gradient of horizontal components of weak solutions. This result improves a recent work by Ni et al. (2012), in the sense that the assumption on the horizontal gradient of the vertical components is removed. As a byproduct, a scaling invariant regularity criterion involving vertical components of vorticity and current density is also obtained. [ABSTRACT FROM AUTHOR]

In this paper, we establish a new regularity criterion for the 3D Navier–Stokes equations via partial components of the fractional derivative. The main result shows that regularity criterion established on the fractional derivatives of u can be almost replaced by several of them. [ABSTRACT FROM AUTHOR]

In this paper we investigate the regularity criterion for the local in time classical solution to the 3D incompressible magnetohydrodynamic equations. We prove that if ∇ × u belongs to L 2 ( 0 , T ; B ̇ ∞ , ∞ − 1 ) , then the local solution ( u , B ) can be extended beyond time T . As a consequence, this result extends several previous works. [ABSTRACT FROM AUTHOR]

We consider the Cauchy problem for the incompressible Navier-Stokes equations in R³, and provide two sufficient conditions to ensure the smoothness of solutions. Both of them only involve two entries of the velocity Hessian tensor. [ABSTRACT FROM AUTHOR]

Abstract: This paper proves two regularity criteria for the density-dependent Hall-MHD system with positive initial density. We also prove a global nonexistence result for initial density with a high decrease at infinity. [Copyright &y& Elsevier]

Abstract: In this note, we consider the regularity problem under the critical condition to the Boussinesq equations with zero heat conductivity. The Serrin type regularity criteria are established in terms of the critical Besov spaces. This improves a result established in a recent work by Geng and Fan (2012) [6]. [Copyright &y& Elsevier]

Abstract: We consider the regularity problem for 3D Navier–Stokes equations in a bounded domain with smooth boundary. A new sufficient condition which guarantees the regularity of weak solutions on the quotient for the Navier–Stokes equations is established. [Copyright &y& Elsevier]

Abstract: This work studies a fluid system with the linear Soret effect. We prove a regularity criterion in the homogeneous Besov space . [Copyright &y& Elsevier]

Abstract: In this paper, we consider the Cauchy problem for a model of electro-hydrodynamics in . When , we prove that the model has a unique global-in-time smooth solution. When , we prove a regularity criterion in terms of the vorticity field only. [Copyright &y& Elsevier]

Abstract: In this work, we prove a regularity criterion for micropolar fluid flows in terms of the pressure in Besov space. [Copyright &y& Elsevier]

Abstract: In this note we prove a regularity criterion for the 3D Boussinesq system with zero thermal conductivity. Here is the velocity, denotes the homogeneous Besov space. [Copyright &y& Elsevier]

Abstract: In this work, a regularity criterion is proved for local strong solutions of the Navier–Stokes equations in the presence of mass diffusion. [Copyright &y& Elsevier]

Abstract: In this note, by using a well-known commutator estimate, we give a new regularity criterion for the 2D dissipative quasi-geostrophic equations in the critical and supercritical cases. [Copyright &y& Elsevier]

Abstract: In this letter, we consider the three-dimensional magnetohydrodynamic (3D MHD) equations and we prove a new regularity criterion for weak solutions. More precisely, we show that if the velocity field with , then the solution remains smooth on . Since for , our result improve the results in He and Xin (2005)  and Zhou (2005) . [Copyright &y& Elsevier]

Abstract: In this note we establish a Serrin-type regularity criterion in terms of pressure for Leray weak solutions to the Navier–Stokes equation in . Here we call a Leray weak solution if is a weak solution of finite energy, i.e. It is known that if a Leray weak solution belongs to then is regular (see [J. Serrin, On the interior regularity of weak solutions of the Navier–Stokes equations, Arch. Ration. Mech. Anal. 9 (1962) 187–195]). We succeed in proving the regularity of the Leray weak solution in terms of pressure under the condition where is the multiplier space (a definition is given in the text) for . Since this space is wider than , the above regularity criterion (0.2) is an improvement on Zhou’s result [Y. Zhou, On regularity criteria in terms of pressure for the Navier–Stokes equations in , Proc. Amer. Math. Soc. 134 (2006) 149–156]. [Copyright &y& Elsevier]

Abstract: In this note we prove a regularity criterion for the 3D Boussinesq system with partial viscosity. Here is the velocity, is the vorticity and denotes the homogeneous Besov space. [Copyright &y& Elsevier]

In this paper we establish a new regularity criterion for the 3D incompressible MHD equations via ∂ 3 u 3 and the magnetic field b. By considering different weights in spatial variables, we show in anisotropic Lebesgue spaces if ∂ 3 u 3 and b satisfy certain space–time integrable conditions, which are almost optimal from the scaling invariant point of view, then a weak solution (u , b) is actually regular. This result gives new insights into the understanding of regularity theory of weak solutions. [ABSTRACT FROM AUTHOR]

We present a new regularity criterion for suitable weak solutions of the one-dimensional surface growth initial-value problem in terms of mixed Lebesgue norms. [ABSTRACT FROM AUTHOR]

In this paper we provide a sufficient condition for regularity of solutions to the 3D nematic liquid crystal flows. More precisely, we prove that if the horizontal velocity component u h = (u 1 , u 2) satisfies ∇ u h ∈ L q (0 , T ; L p (R 3)) , 3 p + 2 q ≤ 3 2 , 2 ≤ p ≤ ∞ , then the solution (u , d) is regular. [ABSTRACT FROM AUTHOR]

In this work, we prove the global well-posedness of strong solutions to the time-dependent Ginzburg–Landau model for superconductivity in R n with 5 ≤ n ≤ 17. [ABSTRACT FROM AUTHOR]