{"paper":{"title":"Instantaneous continuous loss of Sobolev regularity for the 3D incompressible Euler equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"In-Jee Jeong, Luis Mart\\'inez-Zoroa, Wojciech S. O\\.za\\'nski","submitted_at":"2025-08-08T14:08:30Z","abstract_excerpt":"We prove instantaneous and continuous-in-time loss of supercritical Sobolev regularity for the 3D incompressible Euler equations in $\\mathbb{R}^{3}$. Namely, for any $s\\in (0,3/2)$ and $\\varepsilon >0$, we construct a divergence-free initial vorticity $\\omega_0$ defined in $\\mathbb{R}^{3}$ satisfying $\\| \\omega_0 \\|_{H^s}\\leq \\varepsilon$, as well as $T>0$, $c>0$ and a corresponding local-in-time solution $\\omega$ such that, for each $t\\in [0,T]$, $\\omega (\\cdot ,t ) \\in {H^{\\frac{s-ct}{1+ct}}}$ and $ \\omega (\\cdot ,t ) \\not \\in {H^\\beta }$ for any $\\beta > \\frac{s-ct}{1+ct} $. Moreover, $\\ome"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.06333","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/2508.06333/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"}