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In this paper, we find a new regularity criterion of the 3D tropical climate model in terms of one component of the barotropic velocity. Our criteria of the velocity field improve the previous result by Berti et al. Moreover, we extend the regularity criteria of the Lebesgue spaces to that of larger Lorentz spaces. The key of this paper is by using interaction between partial and usual H1$$ {H}^1 $$ estimate to get upper bound of velocities. [ABSTRACT FROM AUTHOR]

In this paper, we derive two regularity criteria of solutions to the nematic liquid crystal flows. More precisely, we prove that the local smooth solution (u,d)$$ \left(u,d\right) $$ is regular if and only if one of the following two conditions is satisfied: (i) ∇huh∈L2p2p−3(0,T;Lp(ℝ3)),∂3d∈L2qq−3(0,T;Lq(ℝ3)),32

In this paper, we establish a new regularity criterion for weak solutions to the 3D incompressible MHD equations in terms of two pairs of (∂iui, ∂ibi)(i=1,2,3). More precisely, it is proved that the weak solution (u, b) is smooth on (0, T], provided that for some i, j ∈ {1, 2, 3} with i ≠ j, it holds that ∂iui,∂juj,∂ibi,∂jbj∈Lp0,T;B˙q,∞0(ℝ3),2p+3q=2,3≤q≤∞. [ABSTRACT FROM AUTHOR]

In this work, we prove some regularity criteria for a Ginzburg‐Landau‐Navier‐Stokes in superfluidity in Rn(n≥3). [ABSTRACT FROM AUTHOR]

In this paper, we study the Cauchy problems for certain regularized models to the incompressible viscoelastic flow in n space dimensions with n=2,3. Firstly, we establish a regularity condition for the solution under ∇u∈L1(0,T;L∞(Rn)). Furthermore, we obtain a regularity condition to the smooth solution for the inviscid regularized models in two space dimensions. Finally, we prove a global existence result of classical solutions for a three‐dimensional incompressible Oldroyd‐α model with fractional diffusion. [ABSTRACT FROM AUTHOR]

By means of the Littlewood‐Paley decomposition and the div‐curl Theorem by Coifman‐Lions‐Meyer‐Semmes, we prove an Osgood type regularity criterion for the 2D incompressible Oldroyd‐B model, that is, sup2≤N<+∞∫0T∑|j|≤N‖Δ˙jτ‖L∞NlogNds,where Δ˙j denotes the Fourier localization operator whose spectrum is supported in the shell {|ξ|≈2j}. [ABSTRACT FROM AUTHOR]

This paper establishes a regularity criterion for the strong solution to the Leray‐α‐MHD in Campanato‐Morrey space. We show that if the magnetic field b satisfies the following condition: ∫0T‖∇b(τ,·)‖M˙qp2p2p−3+‖D2b(τ,·)‖M˙qp2p2p−3dτ<∞, the strong solution (v,b) to the 3‐D Leray‐α MHD equation can be extended beyond T > 0. We also prove that if the magnetic field b satisfies ∫0T‖∇b(τ,·)‖M˙qppp−1dτ<∞, the strong solution (v,b) to the 2‐D Leray‐α MHD equation can be extended beyond T > 0, which extends the results in previous studies. [ABSTRACT FROM AUTHOR]

In this paper, we establish several improved regularity criteria via partial components of vorticity to the incompressible Navier‐Stokes equations in higher dimensions. Our result is a further improvement of the recent result given by Tsurumi [extension criterion via partial components of vorticity on strong solutions to the Navier‐Stokes equations in higher dimensions, J. Differential Equations 263 (2017), 4007‐4022]. [ABSTRACT FROM AUTHOR]

In this paper, we consider the endpoint case regularity for the 3D liquid crystals system. We prove that if v ∈ L ∞ ( 0 , T ; L 3 ( R 3 ) ), then weak solution (v,d) is smooth, and our main observation is that the condition ∇ d ∈ L ∞ ( 0 , T ; L 3 ( R 3 ) ) is not necessary in this situation. The proof is based on the blow‐up analysis and backward uniqueness for the parabolic operator developed by Escauriaza‐Seregin‐S̆verák. [ABSTRACT FROM AUTHOR]

We study the global regularity of classical solution to two-and-half-dimensional magnetohydrodynamic equations with horizontal dissipation and horizontal magnetic diffusion. We prove that any possible finite time blow-up can be controlled by the L ∞-norm of the vertical components. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper is concerned with the short time strong solutions for Cauchy problem to a simplified Ericksen-Leslie system of compressible nematic liquid crystals in two dimensions with vacuum as far field density. We establish a blow-up criterion for possible breakdown of such solutions at a finite time, which is analogous to the well-known Serrin's blow-up criterion for the incompressible Navier-Stokes equations. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Our main object is to establish a regularity criterion [ABSTRACT FROM AUTHOR]

This paper is concerned with the regularity criterion for a class of axisymmetric solutions to 3D incompressible magnetohydrodynamic equations. More precisely, for the solutions that have the form of u = u r e r+ u θ e θ+ u z e z and b = b θ e θ, we prove that if | r u( x, t)|≤ C holds for −1≤ t < 0, then ( u, b) is regular at time zero. This result can be thought as a generalization of recent results in for the 3D incompressible Navier-Stokes equations. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We prove a logarithmic regularity criterion for the 3D generalized magnetohydrodynamics (MHD) system with diffusion terms -?u and (-?)ßb, with 5/2 ≤ ∞. [ABSTRACT FROM AUTHOR]

This paper concerns the 3D Navier-Stokes equations and prove an almost Serrin-type regularity criterion in terms of one directional derivative of the pressure. [ABSTRACT FROM AUTHOR]

We establish a new regularity criterion for the 2D full compressible magnetohydrodynamic system in a bounded domain. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the Cauchy problem for the 3D viscous incompressible magnetohydrodynamic equations and establish a Beale-Kato-Majda regularity criterion of smooth solutions in terms of the velocity vector in the homogeneous bounded mean oscillations space. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we consider sufficient conditions for the regularity of Leray-Hopf solutions of the 3D incompressible magnetohydrodynamic equations via two components of the velocity and magnetic fields in terms of BMO spaces. We prove that if [ABSTRACT FROM AUTHOR]

In this paper, we consider the three-dimensional generalized Boussinesq equations, a system of equations resulting from replacing the Laplacian − Δ in the usual Boussinesq equations by a fractional Laplacian ( − Δ) α. We prove the local existence in time and obtain a regularity criterion of solution for the generalized Boussinesq equations by means of the Littlewood-Paley theory and Bony's paradifferential calculus. The results in this paper can be regarded as an extension to the Serrin-type criteria for Navier-Stokes equations and magnetohydrodynamics equations, respectively. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]