{"paper":{"title":"On the regularity of magneto-vorticity field and the global existence for the Hall magnetohydrodynamic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hantaek Bae, Jaeyong Shin, Kyungkeun Kang","submitted_at":"2024-09-24T08:17:59Z","abstract_excerpt":"In this paper, we investigate the incompressible viscous and resistive Hall magnetohydrodynamic equations (Hall MHD in short). We first study the regularity of the magneto-vorticity field $B+\\omega$. In three dimensions, we derive some bounds of $B+\\omega$ under a condition of the velocity field $u$. Moreover, if we consider the Hall MHD with 2D variables, the uniform-in-time bounds of $B+\\omega$ come from the three dimensional case. The regularity of $B+\\omega$ gives us a crucial clue of blow-up scenario and provides conditions of the existence of global-in-time solutions. In particular, we p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.15847","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/2409.15847/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"}