{"paper":{"title":"Axisymmetric self-similar solutions to the MHD equations without magnetic diffusion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Shaoheng Zhang","submitted_at":"2025-06-25T04:58:43Z","abstract_excerpt":"We study the axisymmetric self-similar solutions $(\\mathbf{u},\\mathbf{B})$ to the stationary MHD equations without magnetic diffusion, where $\\mathbf{B}$ has only the swirl component. Our first result states that in $\\mathbb{R}^3\\setminus\\{0\\}$, $\\mathbf{u}$ is a Landau solution and $\\mathbf{B}=0$. Our second result proves the triviality of axisymmetric self-similar solutions in the half-space $\\mathbb{R}^3_+$ with the no-slip boundary condition or the Navier slip boundary condition."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.20131","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/2506.20131/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"}