The Liouville type theorem for the stationary magnetohydrodynamic equations

Abstract

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.

On Liouville type results for the stationary MHD in R 3

“…On the other hand, Fan and Wang [8] obtained that if a solution (v, b) to (1.1) satisfies b) is identically zero. Recently, Chae et al [3] proved that if for the smooth solution (v, b, P) to the stationary MHD equations satisfies…”

Liouville type theorems for the stationary Hall-MHD equations in local Morrey spaces

“…9.4, pp.729), which proved that if the smooth solution u satisfies u ∈ L 9 2 (R 3 ), 2 ,∞ (R 3 ). For more interesting Liouville type results about MHD and Hall-MHD equations, we refer to [4,7,18,19,25] and the references therein.…”

Liouville type theorems for the stationary Hall‐magnetohydrodynamic equations in local Morrey spaces

“…Recently, the first author and Niu 17 extend the result of Chae et al 16 to the Lorentz space L 9 2 ,∞ ( R 3 ) . For more interesting Liouville type results about MHD and Hall-MHD equations, we refer to previous works [18][19][20][21][22] and the references therein.…”