{"paper":{"title":"A priori estimates and a blow-up criterion for the incompressible ideal MHD equations with surface tension and a closed free surface","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chengchun Hao, Siqi Yang","submitted_at":"2023-12-15T01:20:45Z","abstract_excerpt":"We establish the a priori estimates and prove a blow-up criterion for the three-dimensional free boundary incompressible ideal magnetohydrodynamics equations. The fluid occupies a bounded region with a free boundary that is a closed surface, without assumptions of simple connectedness or periodicity of the region (thus, Fourier transforms cannot be applied), nor the graph assumption for the free boundary. The fluid is under the influence of surface tension, and flattening the boundaries using local coordinates is insufficient to resolve this problem. This is because local coordinates fail to p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.09473","kind":"arxiv","version":4},"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/2312.09473/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"}