相关论文: On some Liouville type Theorems for the stationary…
We prove several Liouville type results for the stationary Hall-MHD and MHD equations. In particular, we show that the velocity and magnetic field, belonging to some Lorentz spaces, must be zero.
In this note we investigate Liouville type theorems for the steady three dimensional MHD and Hall-MHD equations, and show that the velocity field $u$ and the magnetic field $B$ are vanishing provided that $B\in L^{6,\infty}(\mathbb{R}^3)$…
In this paper, we investigate Liouville type theorems for the three-dimensional steady-state MHD or Hall-MHD system under some asymptotic assumptions at infinity. Firstly, for the Hall-MHD system we obtain that $u$ and $B$ are constant…
This paper is concerned with the Liouville type theorems for the 3D stationary incompressible Hall-MHD equations. We establish that under some sufficient conditions in local Morrey spaces, solutions of the stationary Hall-MHD equations are…
For the two dimensional stationary MHD equations, we proved that Liouville type theorems hold if the velocity is growing at infinity, where the magnetic field is assumed to be bounded under a smallness condition. The key point is to…
We show that any smooth solution $(\mathbf{u},\mathbf{H})$ to the stationary equations of magneto-hydrodynamics (MHD) belonging to both spaces $L^6 (\mathbb{R}^3)$ and $BMO^{-1}(\mathbb{R}^3)$ must be identically zero. This is an extension…
In this paper, we study Liouville type results for the three-dimensional stationary incompressible MHD equations and Hall-MHD equations. Using the energy method and an iteration argument, we establish Liouville type theorems if Lebesgue…
In this paper we prove a Liouville type theorem for the stationary MHD and the stationary Hall-MHD systems. Assuming suitable growth condition at infinity for the mean oscillations for the potential functions, we show that the solutions are…
In this paper, we study the Liouville--type theorems for three--dimensional stationary incompressible MHD and Hall--MHD systems in a slab with periodic boundary condition. We show that, under the assumptions that $(u^\theta,b^\theta)$ or…
This note is devoted to investigating Liouville type properties of the two dimensional stationary incompressible Magnetohydrodynamics equations. More precisely, under smallness conditions only on the magnetic field, we show that there are…
The Liouville problem for the stationary Navier-Stokes equations on the whole space is a challenging open problem who has know several recent contributions. We prove here some Liouville type theorems for these equations provided the…
In this paper we prove a Liouville type theorem for the stationary magnetohydrodynamics(MHD) system in $\Bbb R^3$. Let $(v, B, p)$ be a smooth solution to the stationary MHD equations in $\Bbb R^3$. We show that if there exist smooth matrix…
In this paper, we study the stationary magnetohydrodynamics system in $\mathbb{R}^2\times\mathbb{T}$. We prove trivialness of D-solutions (the velocity field $u$ and the magnetic field $h$) when they are swirl-free. Meanwhile, this…
It is shown that any smooth solution to the stationary Navier-Stokes system in $R^3$ with the velocity field, belonging globally to $L_6$ and $BM0^{-1}$, must be zero.
Our aim is to prove Liouville type theorems for the three dimensional steady-state Navier-Stokes equations provided the velocity field belongs to some Lorentz spaces. The corresponding statement contains several known results as a…
In this paper we prove Liouville type theorem for the double Beltrami solutions to the stationary Hall-MHD equations in $\Bbb R^3$. Let $(u, B)$ be a smooth double Beltrami solution to the stationary Hall-MHD equations in $\Bbb R^3$,…
We establish new Liouville-type theorems for the two-dimensional stationary magneto-hydrodynamic incompressible system assuming that the velocity and magnetic field have bounded Dirichlet integral. The key tool in our proof is observing…
We research the Liouville type problem for the 3D stationary MHD equations in the frequency space. We establish two new Liouville type theorems for solutions with finite Dirichlet energy. Specifically, we show that the low-frequency part of…
In this note, we investigate the 3D steady axially symmetric Navier-Stokes equations, and obtained Liouville type theorems if the velocity or the vorticity satisfies some a priori decay assumptions.
In this paper we prove Liouville type theorem for the stationary Navier-Stokes equations in $\Bbb R^3$ under the assumptions on the relative decays of velocity, pressure and the head pressure. More precisely, we show that any smooth…