Liouville Type Theorem for the Steady Fractional Compressible MHD Equations in ${\mathbb{R}}^3$

Abstract

This paper is concerned with the Liouville-type problem for the stationary fractional compressible magnetohydrodynamics (MHD) equations. The main difficulty comes from the nonlocal fractional Laplace operator $(-\Delta {)}^s$. To overcome it, we combine the Caffarelli-Silvestre extension technique with truncation arguments. Under suitable regularity and decay conditions, we prove that the only solution is trivial, establishing a Liouville-type theorem.

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