{"paper":{"title":"Liouville Type Theorem for the Steady Fractional Compressible MHD Equations in $\\mathbb{R}^{3}$","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Weihua Wang, Zhenyuan Liu","submitted_at":"2026-05-30T12:48:48Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.00713","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.00713/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}