{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:6GDNEXUB6THXELH7ANZR2OM2YE","short_pith_number":"pith:6GDNEXUB","schema_version":"1.0","canonical_sha256":"f186d25e81f4cf722cff03731d399ac101f72076b242951a3bc08b7b9a64c075","source":{"kind":"arxiv","id":"math/0608541","version":1},"attestation_state":"computed","paper":{"title":"Confinement of vorticity in two dimensional ideal incompressible exterior flow","license":"","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"D. Iftimie, H. J. Nussenzveig Lopes, M. C. Lopes Filho","submitted_at":"2006-08-22T12:09:40Z","abstract_excerpt":"In [Math. Meth. Appl. Sci. 19 (1996) 53-62], C. Marchioro examined the problem of vorticity confinement in the exterior of a smooth bounded domain. The main result in Marchioro's paper is that solutions of the incompressible 2D Euler equations with compactly supported nonnegative initial vorticity in the exterior of a connected bounded region have vorticity support with diameter growing at most like $\\mathcal{O}(t^{(1/2)+\\vare})$, for any $\\vare>0$. In addition, if the domain is the exterior of a disk, then the vorticity support is contained in a disk of radius $\\mathcal{O}(t^{1/3})$. The purp"},"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":"math/0608541","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AP","submitted_at":"2006-08-22T12:09:40Z","cross_cats_sorted":[],"title_canon_sha256":"0703ebabcbe8820acc555b7708e5dd7cf392f94d5d44b703042d4de36a144ee6","abstract_canon_sha256":"0e5f589052f40e09d457cff4d5c50ac1ad4b459de1ecd3eb68df251edb4a2560"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:08:53.300645Z","signature_b64":"lriL9hi3Z4XWaL69zCxnlkmyWGpbycLka4JmVuVVqRNtlQbeDfsxk0kC7wlVWtMJo1IcohkVIWNFsDdHHxXtCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f186d25e81f4cf722cff03731d399ac101f72076b242951a3bc08b7b9a64c075","last_reissued_at":"2026-05-18T04:08:53.299910Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:08:53.299910Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Confinement of vorticity in two dimensional ideal incompressible exterior flow","license":"","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"D. Iftimie, H. J. Nussenzveig Lopes, M. C. Lopes Filho","submitted_at":"2006-08-22T12:09:40Z","abstract_excerpt":"In [Math. Meth. Appl. Sci. 19 (1996) 53-62], C. Marchioro examined the problem of vorticity confinement in the exterior of a smooth bounded domain. The main result in Marchioro's paper is that solutions of the incompressible 2D Euler equations with compactly supported nonnegative initial vorticity in the exterior of a connected bounded region have vorticity support with diameter growing at most like $\\mathcal{O}(t^{(1/2)+\\vare})$, for any $\\vare>0$. In addition, if the domain is the exterior of a disk, then the vorticity support is contained in a disk of radius $\\mathcal{O}(t^{1/3})$. The purp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0608541","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"math/0608541","created_at":"2026-05-18T04:08:53.300016+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0608541v1","created_at":"2026-05-18T04:08:53.300016+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0608541","created_at":"2026-05-18T04:08:53.300016+00:00"},{"alias_kind":"pith_short_12","alias_value":"6GDNEXUB6THX","created_at":"2026-05-18T12:25:53.939244+00:00"},{"alias_kind":"pith_short_16","alias_value":"6GDNEXUB6THXELH7","created_at":"2026-05-18T12:25:53.939244+00:00"},{"alias_kind":"pith_short_8","alias_value":"6GDNEXUB","created_at":"2026-05-18T12:25:53.939244+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6GDNEXUB6THXELH7ANZR2OM2YE","json":"https://pith.science/pith/6GDNEXUB6THXELH7ANZR2OM2YE.json","graph_json":"https://pith.science/api/pith-number/6GDNEXUB6THXELH7ANZR2OM2YE/graph.json","events_json":"https://pith.science/api/pith-number/6GDNEXUB6THXELH7ANZR2OM2YE/events.json","paper":"https://pith.science/paper/6GDNEXUB"},"agent_actions":{"view_html":"https://pith.science/pith/6GDNEXUB6THXELH7ANZR2OM2YE","download_json":"https://pith.science/pith/6GDNEXUB6THXELH7ANZR2OM2YE.json","view_paper":"https://pith.science/paper/6GDNEXUB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0608541&json=true","fetch_graph":"https://pith.science/api/pith-number/6GDNEXUB6THXELH7ANZR2OM2YE/graph.json","fetch_events":"https://pith.science/api/pith-number/6GDNEXUB6THXELH7ANZR2OM2YE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6GDNEXUB6THXELH7ANZR2OM2YE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6GDNEXUB6THXELH7ANZR2OM2YE/action/storage_attestation","attest_author":"https://pith.science/pith/6GDNEXUB6THXELH7ANZR2OM2YE/action/author_attestation","sign_citation":"https://pith.science/pith/6GDNEXUB6THXELH7ANZR2OM2YE/action/citation_signature","submit_replication":"https://pith.science/pith/6GDNEXUB6THXELH7ANZR2OM2YE/action/replication_record"}},"created_at":"2026-05-18T04:08:53.300016+00:00","updated_at":"2026-05-18T04:08:53.300016+00:00"}