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### Open Access Journals

PROC

The global Cauchy problem for an approximation model for the
ideal density-dependent MHD-$\alpha$ model is studied. The vanishing limit on is
also discussed.

PROC

The global Cauchy problem for an approximation model for the
density-dependent MHD system is studied. The vanishing limit on
$\alpha$ is also discussed.

PROC

This paper proves a regularity criterion $\nabla u,\nabla b\in L^\infty(0,T;L^\infty)$
for 3D density-dependent MHD system with zero viscosity and positive initial density.

CPAA

We study the $n$-dimensional magnetohydrodynamic-$\alpha$
(MHD-$\alpha$) model in the whole space. Various regularity criteria
are established. When $n=4$, uniqueness of weak solutions is also
proved. As a corollary, the strong solution to this model exists
globally, as $n \leq 4$.

CPAA

In this paper, we study the large-time behavior of weak solutions to the initial-boundary problem arising in a simplified
Ericksen-Leslie system for nonhomogeneous incompressible flows of nematic liquid crystals
with a transformation condition of trigonometric functions (called by trigonometric condition for simplicity) posed on the initial direction field in a bounded domain $\Omega\subset \mathbb{R}^2$.
We show that the kinetic energy and direction field converge to zero and an equilibrium state,
respectively, as time goes to infinity. Further, if the initial density is away from vacuum and bounded, then the density, and velocity and direction fields exponential decay to an equilibrium state. In addition, we also show that the weak solutions of the corresponding compressible flows
converge {an equilibrium} state.

KRM

We prove some regularity conditions for the MHD equations with
partial viscous terms and the Leray-$\alpha$-MHD model. Since the
solutions to the Leray-$\alpha$-MHD model are smoother than that of
the original MHD equations, we are able to obtain better regularity
conditions in terms of the magnetic field $B$ only.

DCDS

We consider the hydrodynamic theory of liquid crystals. We prove
some regularity criteria for a simplified Ericksen-Leslie system.
The existence and uniqueness of global smooth solutions is also
proved for a regularization model of this simplified system.

KRM

This paper proves some regularity criteria for the 2D MHD system with horizontal dissipation and horizontal
magnetic diffusion. We also prove the global existence of strong solutions of its regularized MHD-$\alpha$ system.

CPAA

In this paper, we prove some logarithmically improved regularity
criteria for the 3D nematic liquid crystals models, Boussinesq
system, and MHD equations in a bounded domain.

CPAA

We prove local in time existence and uniqueness of solutions of the
ideal inhomogeneous magnetohydrodynamic equations.

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