| Abstract: |
| We establish Liouville-type theorems for the stationary ideal compressible magnetohydrodynamics system in $\mathbb{R}^n$ with $n\in\{1, 2, 3\}$. We address various cases when the finite energy condition is in force and the stationary density function $\rho$ satisfies $\lim_{|x|\to\infty}\rho(x)=\rho_\infty\ge0$. 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. |
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