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

Zhenyuan Liu; Weihua Wang

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arXiv · 2606.00713

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

Zhenyuan Liu·Weihua Wang

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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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Zhenyuan Liu, Weihua Wang. 2026-05-30. Liouville Type Theorem for the Steady Fractional Compressible MHD Equations in $\mathbb{R}^{3}$. https://arxiv.org/abs/2606.00713

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