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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2508.06333","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-08-08T14:08:30Z","cross_cats_sorted":[],"title_canon_sha256":"eadffc4ac5201e1f2a74936c7bb6df7fe6f20e8511503e434ef9ff4bd77f0d07","abstract_canon_sha256":"73be5af95768ee0434fcf23b3b81b213bc5740feb0a074c4534c03d7850ac256"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:50:54.424433Z","signature_b64":"/HTpZLpBcoozQsvOW3rhOpjrISfuPlcmxghxngPeOqeHWJB2KJCU4pld1vxYtvf62+JEkgUQiTxA7L2ElSnzDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c920d3bf834e88e0df57acae47a8abe94249b1f61b4919ddd332ab56292a815f","last_reissued_at":"2026-07-05T11:50:54.423801Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:50:54.423801Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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} $. 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