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This paper poses a new question and proves a related result. Particularly, the nonexistence of a nontrivial time-periodic solution to the Navier–Stokes system is proved in a bounded domain in R² . [ABSTRACT FROM AUTHOR]

First, we prove uniform-in-e regularity estimates of local strong solutions to the ChernSimons-Schrodinger equations in ¨ R ² . Here e is the dispersion coefficient. Then we prove the global well-posedness of strong solutions to the limit problem (e = 0). [ABSTRACT FROM AUTHOR]

In this paper, we will use the Banach fixed point theorem to prove the uniform-in-ϵ existence of the compressible full magneto-micropolar system in a bounded smooth domain, where ϵ is the dielectric constant. Consequently, the limit as ϵ→0 can be established. This approximation is usually referred to as the magnetohydrodynamics approximation and is equivalent to the neglect of the displacement current. [ABSTRACT FROM AUTHOR]

In this paper we study the low Mach number limit of the full compressible Hall-magnetohydrodynamic (Hall-MHD) system in T³. We prove that, as the Mach number tends to zero, the strong solution of the full com- pressible Hall-MHD system converges to that of the incompressible Hall-MHD system [ABSTRACT FROM AUTHOR]

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 ows 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 Ω ⊂R2. 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 ows converge an equilibrium state. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper we establish the global existence of strong solution to the density-dependent incompressible magnetohydrodynamic equations with vaccum in a bounded domain in ℝ². Furthermore, the limit as the heat conductivity coefficient tends to zero is also obtained. [ABSTRACT FROM AUTHOR]