On the Vanishing of Some D-Solutions to the Stationary Magnetohydrodynamics System

In this paper, we study Liouville theorems of D-solutions to the stationary magnetohydrodynamic system in a slab. We will prove trivialness of the velocity and the magnetic field with various boundary conditions. In some boundary conditions, the additional assumption that the horizontal angular component(s) of the velocity or (and) the magnetic field is (are) axially symmetric is needed. More precisely, five types of boundary conditions will be considered: the vertical periodic boundary condition for the velocity and the magnetic field, the Navier-slip boundary condition for the velocity, the perfectly conducting or insulating boundary condition for the magnetic field, the non-slip boundary condition for the velocity, and the perfectly conducting or insulating boundary condition for the magnetic field. One of our innovations is that we do not impose finite Dirichlet integral assumption on the magnetic field compared with previous works.

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The Liouville type theorem for the stationary magnetohydrodynamic equations

Fan

Wang

2021

Journal of Mathematical Physics

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In this paper, we focused on demonstrating the Liouville type theorem for the stationary magnetohydrodynamic equations. First, we improve the well-known L92(R3) result logarithmically. In addition, we are aimed to an asymptotic formula for an integral involving the total head pressure Q=12|u|2+|h|2+p and its derivative over domains enclosed by level surfaces of Q, which provides us with the additional sufficient condition for the triviality of solution for the magnetohydrodynamic equations.

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On the Vanishing of Some D-Solutions to the Stationary Magnetohydrodynamics System

Cited by 3 publications

References 19 publications

Liouville-type theorems for steady MHD and Hall-MHD equations in R2×T

Liouville-type theorems for steady MHD and Hall-MHD equations in R2×T

Liouville theorem of D-solutions to the stationary magnetohydrodynamics system in a slab

The Liouville type theorem for the stationary magnetohydrodynamic equations

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