PROC
Global Cauchy problem of an ideal density-dependent MHD-$\alpha$ model
Jishan Fan Tohru Ozawa
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.
keywords: ideal density-dependent MHD-$\alpha$
PROC
An approximation model for the density-dependent magnetohydrodynamic equations
Jishan Fan Tohru Ozawa
The global Cauchy problem for an approximation model for the density-dependent MHD system is studied. The vanishing limit on $\alpha$ is also discussed.
keywords: MHD-alpha. MHD Density-dependent
PROC
A regularity criterion for 3D density-dependent MHD system with zero viscosity
Jishan Fan Tohru Ozawa
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.
keywords: MHD ideal fluid. regularity criterion
CPAA
Regularity criteria for a magnetohydrodynamic-$\alpha$ model
Yong Zhou Jishan Fan
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 $n \leq 4$.
keywords: 76D03. Primary: 35B40
CPAA
Large-time behavior of liquid crystal flows with a trigonometric condition in two dimensions
Jishan Fan Fei Jiang
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.
keywords: Liquid crystals weak solutions exponential decay Navier-Stokes equations. large-time behavior
KRM
Regularity criteria for the magnetohydrodynamic equations with partial viscous terms and the Leray-$\alpha$-MHD model
Jishan Fan Tohru Ozawa
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.
keywords: MHD equations regularity criterion interpolation inequality in Besov spaces. Leray-$\alpha$-MHD model
DCDS
Regularity criteria for a simplified Ericksen-Leslie system modeling the flow of liquid crystals
Jishan Fan Tohru Ozawa
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.
keywords: liquid crystals Ericksen-Leslie system regularity condition Navier-Stokes equations.
KRM
Regularity criteria for the 2D MHD system with horizontal dissipation and horizontal magnetic diffusion
Jishan Fan Tohru Ozawa
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.
keywords: MHD regularity criterion BMO space.
CPAA
Logarithmic and improved regularity criteria for the 3D nematic liquid crystals models, Boussinesq system, and MHD equations in a bounded domain
Luigi C. Berselli Jishan Fan
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.
keywords: Regularity criteria MHD Boussinesq equations liquid crystals
CPAA
Local well-posedness for the ideal incompressible density dependent magnetohydrodynamic equations
Yong Zhou Jishan Fan
We prove local in time existence and uniqueness of solutions of the ideal inhomogeneous magnetohydrodynamic equations.
keywords: local existence inhomogeneous Euler equations. Ideal inhomogeneous MHD

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