Liouville Type Theorem for the Fractional MHD and Hall-MHD equations in $\mathbb{R}^{3}

Weihua Wang; Zhenyuan Liu

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arXiv · 2602.00584

Liouville Type Theorem for the Fractional MHD and Hall-MHD equations in $\mathbb{R}^{3}

Weihua Wang·Zhenyuan Liu

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Abstract

In this paper, we are mainly concerned with the Liouville type problem for the stationary fractional magnetohydrodynamics(MHD) and stationary fractional Hall-MHD equations. In addition, we present the results of the Navier-Stokes equation as a byproduct. The key point is to use the Caffarelli-Sivestre extension to overcome the difficulty caused by the non-local operator $(-\triangle)^{s}$ and combined with Yuan and Xiao's method (J. Math. Anal. Appl. 491 (2020) 124343).

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Weihua Wang, Zhenyuan Liu. 2026-01-31. Liouville Type Theorem for the Fractional MHD and Hall-MHD equations in $\mathbb{R}^{3}. https://arxiv.org/abs/2602.00584

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