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By establishing the gradient estimate of $u$, $\\tau$ and $L^\\infty$ bound of ${\\rm curl u+\\Lambda^{-2}curldiv \\tau}$, Elgidi-Rousset (Commun. Pure Appl. Math. online, 2015) obtained the global well-posedness for the case $\\nu=0$, $\\beta=1$. However, for the cases $(i)$ and $(ii)$, it is difficult to improve the regularity of $u$ and $\\tau$ directly, especially when $\\alpha\\rightarrow 1^{+}$ in case $(i)"},"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":"1509.07663","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-25T10:26:39Z","cross_cats_sorted":[],"title_canon_sha256":"5e84a19bd668b2be53982fbada4eb44ae4235fd7fd6fdc40bfe308977b0b3538","abstract_canon_sha256":"4820cfcfa129d6ce3dd022027f45f9c270d5c3a3eb876dc534e0be266651a28e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:31:52.600571Z","signature_b64":"C1CBrEsbR2nkvKzpRgw8r55CR5Fnn84JfcFiDjnP5KaeUSAgkZuEIW72rz7GSNSa6B5N3jBLhtrT8fD2MBEODg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"132cbd6cf558b8a1a32f5826507e1f34df60880e0be74115b6e88150b1ed1762","last_reissued_at":"2026-05-18T01:31:52.600095Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:31:52.600095Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Global well-posedness to the subcritical Oldroyd-B type models in 2D","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Renhui Wan","submitted_at":"2015-09-25T10:26:39Z","abstract_excerpt":"We prove the global well-posedness to the 2D Oldroyd-B type models with $\\nu \\Lambda^{2\\alpha}u$ and $\\eta\\Lambda^{2\\beta}\\tau$ satisfying $(i)\\ \\alpha>1, \\eta=0$ or $(ii)\\ \\alpha=1,\\ \\beta>0$. By establishing the gradient estimate of $u$, $\\tau$ and $L^\\infty$ bound of ${\\rm curl u+\\Lambda^{-2}curldiv \\tau}$, Elgidi-Rousset (Commun. Pure Appl. Math. online, 2015) obtained the global well-posedness for the case $\\nu=0$, $\\beta=1$. However, for the cases $(i)$ and $(ii)$, it is difficult to improve the regularity of $u$ and $\\tau$ directly, especially when $\\alpha\\rightarrow 1^{+}$ in case $(i)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07663","kind":"arxiv","version":2},"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":"1509.07663","created_at":"2026-05-18T01:31:52.600176+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.07663v2","created_at":"2026-05-18T01:31:52.600176+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.07663","created_at":"2026-05-18T01:31:52.600176+00:00"},{"alias_kind":"pith_short_12","alias_value":"CMWL23HVLC4K","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_16","alias_value":"CMWL23HVLC4KDIZP","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_8","alias_value":"CMWL23HV","created_at":"2026-05-18T12:29:17.054201+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/CMWL23HVLC4KDIZPLATFA7Q7GT","json":"https://pith.science/pith/CMWL23HVLC4KDIZPLATFA7Q7GT.json","graph_json":"https://pith.science/api/pith-number/CMWL23HVLC4KDIZPLATFA7Q7GT/graph.json","events_json":"https://pith.science/api/pith-number/CMWL23HVLC4KDIZPLATFA7Q7GT/events.json","paper":"https://pith.science/paper/CMWL23HV"},"agent_actions":{"view_html":"https://pith.science/pith/CMWL23HVLC4KDIZPLATFA7Q7GT","download_json":"https://pith.science/pith/CMWL23HVLC4KDIZPLATFA7Q7GT.json","view_paper":"https://pith.science/paper/CMWL23HV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.07663&json=true","fetch_graph":"https://pith.science/api/pith-number/CMWL23HVLC4KDIZPLATFA7Q7GT/graph.json","fetch_events":"https://pith.science/api/pith-number/CMWL23HVLC4KDIZPLATFA7Q7GT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CMWL23HVLC4KDIZPLATFA7Q7GT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CMWL23HVLC4KDIZPLATFA7Q7GT/action/storage_attestation","attest_author":"https://pith.science/pith/CMWL23HVLC4KDIZPLATFA7Q7GT/action/author_attestation","sign_citation":"https://pith.science/pith/CMWL23HVLC4KDIZPLATFA7Q7GT/action/citation_signature","submit_replication":"https://pith.science/pith/CMWL23HVLC4KDIZPLATFA7Q7GT/action/replication_record"}},"created_at":"2026-05-18T01:31:52.600176+00:00","updated_at":"2026-05-18T01:31:52.600176+00:00"}