Liouville Type Theorem for the Fractional MHD and Hall-MHD equations in $\mathbb{R}^{3}
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| Format: | Preprint |
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2026
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| _version_ | 1866908892721577984 |
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| author | Wang, Weihua Liu, Zhenyuan |
| author_facet | Wang, Weihua Liu, Zhenyuan |
| contents | 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). |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_00584 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Liouville Type Theorem for the Fractional MHD and Hall-MHD equations in $\mathbb{R}^{3} Wang, Weihua Liu, Zhenyuan Analysis of PDEs 35Q35, 76D03 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). |
| title | Liouville Type Theorem for the Fractional MHD and Hall-MHD equations in $\mathbb{R}^{3} |
| topic | Analysis of PDEs 35Q35, 76D03 |
| url | https://arxiv.org/abs/2602.00584 |