Liouville-Type Theorems for the Stationary Ideal Magnetohydrodynamics Equations in \(\textbf{R}^n\)

In this paper, we establish Liouville-type theorems for the stationary ideal compressible magnetohydrodynamics system in \(\textbf{R}^n\) ${\mathbf{R}}^n$ with \(n\in \{1, 2, 3\}\) $n\in \{1,2,3\}$ . We address various cases when the finite energy condition is in force and the stationary density function \(\rho \) $\rho$ satisfies \(\displaystyle \lim _{|x|\rightarrow \infty }\rho (x)=\rho _\infty \ge 0\) ${\displaystyle \underset{|x|\to \infty }{lim}\rho (x)={\rho }_{\infty }\ge 0}$ . Our proof relies heavily on the good structure of the nonlinear magnetic force term and the usage of well-chosen smooth cut-off test functions.