Liouville Type Theorem for the Steady Fractional Compressible MHD Equations in $\mathbb{R}^{3}$
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917550334410752 |
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| author | Liu, Zhenyuan Wang, Weihua |
| author_facet | Liu, Zhenyuan Wang, Weihua |
| contents | 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 $(-Δ)^s$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_00713 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Liouville Type Theorem for the Steady Fractional Compressible MHD Equations in $\mathbb{R}^{3}$ Liu, Zhenyuan Wang, Weihua Analysis of PDEs 76W03, 35B53, 26A33, 35Q35 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 $(-Δ)^s$. 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. |
| title | Liouville Type Theorem for the Steady Fractional Compressible MHD Equations in $\mathbb{R}^{3}$ |
| topic | Analysis of PDEs 76W03, 35B53, 26A33, 35Q35 |
| url | https://arxiv.org/abs/2606.00713 |