{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:2PECVVY6CJPPUE2TTZSTGN2HEQ","short_pith_number":"pith:2PECVVY6","schema_version":"1.0","canonical_sha256":"d3c82ad71e125efa13539e65333747241fc4d43a22075de4bc5d12a771a0aece","source":{"kind":"arxiv","id":"1709.00774","version":2},"attestation_state":"computed","paper":{"title":"On the Viscous Camassa-Holm Equations with Fractional Diffusion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fang-Hua Lin, Jiajun Tong, Zaihui Gan","submitted_at":"2017-09-03T23:03:17Z","abstract_excerpt":"We study Cauchy problem of a class of viscous Camassa-Holm equations (or Lagrangian averaged Navier-Stokes equations) with fractional diffusion in both smooth bounded domains and in the whole space in two and three dimensions. Order of the fractional diffusion is assumed to be $2s$ with $s\\in [n/4,1)$, which seems to be sharp for the validity of the main results of the paper; here $n=2,3$ is the dimension of space. We prove global well-posedness in $C_{[0,+\\infty)}(D(A))\\cap L^2_{[0,+\\infty),loc}(D(A^{1+s/2}))$ whenever the initial data $u_0\\in D(A)$, where $A$ is the Stokes operator. We also "},"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":"1709.00774","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-03T23:03:17Z","cross_cats_sorted":[],"title_canon_sha256":"917dd858b68d7faea9b00cce035c2c8358b5cb6a79bbdfedd3641a7171525405","abstract_canon_sha256":"97beb1fc838d2af360c95133fb1d75c2649c805f94de26673b75cc31424a4b67"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:54.113620Z","signature_b64":"TE/Fr7Wb5/ZfJoPsUyi/GsE1O9XDIgDY8yxkbPSOzWtf555oh2+PhO599BwaYtLEfJTkwQKgVsWdKPR0ck5GBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d3c82ad71e125efa13539e65333747241fc4d43a22075de4bc5d12a771a0aece","last_reissued_at":"2026-05-17T23:43:54.112944Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:54.112944Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Viscous Camassa-Holm Equations with Fractional Diffusion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fang-Hua Lin, Jiajun Tong, Zaihui Gan","submitted_at":"2017-09-03T23:03:17Z","abstract_excerpt":"We study Cauchy problem of a class of viscous Camassa-Holm equations (or Lagrangian averaged Navier-Stokes equations) with fractional diffusion in both smooth bounded domains and in the whole space in two and three dimensions. Order of the fractional diffusion is assumed to be $2s$ with $s\\in [n/4,1)$, which seems to be sharp for the validity of the main results of the paper; here $n=2,3$ is the dimension of space. We prove global well-posedness in $C_{[0,+\\infty)}(D(A))\\cap L^2_{[0,+\\infty),loc}(D(A^{1+s/2}))$ whenever the initial data $u_0\\in D(A)$, where $A$ is the Stokes operator. We also "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.00774","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":"1709.00774","created_at":"2026-05-17T23:43:54.113035+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.00774v2","created_at":"2026-05-17T23:43:54.113035+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.00774","created_at":"2026-05-17T23:43:54.113035+00:00"},{"alias_kind":"pith_short_12","alias_value":"2PECVVY6CJPP","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_16","alias_value":"2PECVVY6CJPPUE2T","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_8","alias_value":"2PECVVY6","created_at":"2026-05-18T12:30:55.937587+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/2PECVVY6CJPPUE2TTZSTGN2HEQ","json":"https://pith.science/pith/2PECVVY6CJPPUE2TTZSTGN2HEQ.json","graph_json":"https://pith.science/api/pith-number/2PECVVY6CJPPUE2TTZSTGN2HEQ/graph.json","events_json":"https://pith.science/api/pith-number/2PECVVY6CJPPUE2TTZSTGN2HEQ/events.json","paper":"https://pith.science/paper/2PECVVY6"},"agent_actions":{"view_html":"https://pith.science/pith/2PECVVY6CJPPUE2TTZSTGN2HEQ","download_json":"https://pith.science/pith/2PECVVY6CJPPUE2TTZSTGN2HEQ.json","view_paper":"https://pith.science/paper/2PECVVY6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.00774&json=true","fetch_graph":"https://pith.science/api/pith-number/2PECVVY6CJPPUE2TTZSTGN2HEQ/graph.json","fetch_events":"https://pith.science/api/pith-number/2PECVVY6CJPPUE2TTZSTGN2HEQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2PECVVY6CJPPUE2TTZSTGN2HEQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2PECVVY6CJPPUE2TTZSTGN2HEQ/action/storage_attestation","attest_author":"https://pith.science/pith/2PECVVY6CJPPUE2TTZSTGN2HEQ/action/author_attestation","sign_citation":"https://pith.science/pith/2PECVVY6CJPPUE2TTZSTGN2HEQ/action/citation_signature","submit_replication":"https://pith.science/pith/2PECVVY6CJPPUE2TTZSTGN2HEQ/action/replication_record"}},"created_at":"2026-05-17T23:43:54.113035+00:00","updated_at":"2026-05-17T23:43:54.113035+00:00"}