{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:KPCPTHX36PIV6YLOVZS4NKDDTV","short_pith_number":"pith:KPCPTHX3","schema_version":"1.0","canonical_sha256":"53c4f99efbf3d15f616eae65c6a8639d4ae045e14ef29dcd78b905c5bf8351cb","source":{"kind":"arxiv","id":"1310.2141","version":2},"attestation_state":"computed","paper":{"title":"Analyticity for the (generalized) Navier-Stokes equations with rough initial data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Baoxiang Wang, Chunyan Huang","submitted_at":"2013-10-08T14:09:50Z","abstract_excerpt":"We study the Cauchy problem for the (generalized) incompressible Navier-Stokes equations \\begin{align} u_t+(-\\Delta)^{\\alpha}u+u\\cdot \\nabla u +\\nabla p=0, \\ \\ {\\rm div} u=0, \\ \\ u(0,x)= u_0. \\nonumber \\end{align} We show the analyticity of the local solutions of the Navier-Stokes equation ($\\alpha=1$) with any initial data in critical Besov spaces $\\dot{B}^{n/p-1}_{p,q}(\\mathbb{R}^n)$ with $1< p<\\infty, \\ 1\\le q\\le \\infty $ and the solution is global if $u_0$ is sufficiently small in $\\dot{B}^{n/p-1}_{p,q}(\\mathbb{R}^n)$. In the case $p=\\infty$, the analyticity for the local solutions of the "},"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":"1310.2141","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-08T14:09:50Z","cross_cats_sorted":[],"title_canon_sha256":"c43e0489de29a864550a42bdd483022f94bfb068784acae95c3c49836482f969","abstract_canon_sha256":"e4926eb3117953171273a0c2d1208ccf48a8940faf2ecdbc07e8cd3e28312381"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:08:24.562943Z","signature_b64":"52eSrJuouba+bg+sAonq/+XpCPjXxdOtmbV2/WsoKC4mgv+wxpPb42EvsqS6x+357nb8/VpoSka+yKHhWXXlAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"53c4f99efbf3d15f616eae65c6a8639d4ae045e14ef29dcd78b905c5bf8351cb","last_reissued_at":"2026-05-18T03:08:24.562335Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:08:24.562335Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Analyticity for the (generalized) Navier-Stokes equations with rough initial data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Baoxiang Wang, Chunyan Huang","submitted_at":"2013-10-08T14:09:50Z","abstract_excerpt":"We study the Cauchy problem for the (generalized) incompressible Navier-Stokes equations \\begin{align} u_t+(-\\Delta)^{\\alpha}u+u\\cdot \\nabla u +\\nabla p=0, \\ \\ {\\rm div} u=0, \\ \\ u(0,x)= u_0. \\nonumber \\end{align} We show the analyticity of the local solutions of the Navier-Stokes equation ($\\alpha=1$) with any initial data in critical Besov spaces $\\dot{B}^{n/p-1}_{p,q}(\\mathbb{R}^n)$ with $1< p<\\infty, \\ 1\\le q\\le \\infty $ and the solution is global if $u_0$ is sufficiently small in $\\dot{B}^{n/p-1}_{p,q}(\\mathbb{R}^n)$. In the case $p=\\infty$, the analyticity for the local solutions of the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.2141","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":"1310.2141","created_at":"2026-05-18T03:08:24.562424+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.2141v2","created_at":"2026-05-18T03:08:24.562424+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.2141","created_at":"2026-05-18T03:08:24.562424+00:00"},{"alias_kind":"pith_short_12","alias_value":"KPCPTHX36PIV","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_16","alias_value":"KPCPTHX36PIV6YLO","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_8","alias_value":"KPCPTHX3","created_at":"2026-05-18T12:27:51.066281+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/KPCPTHX36PIV6YLOVZS4NKDDTV","json":"https://pith.science/pith/KPCPTHX36PIV6YLOVZS4NKDDTV.json","graph_json":"https://pith.science/api/pith-number/KPCPTHX36PIV6YLOVZS4NKDDTV/graph.json","events_json":"https://pith.science/api/pith-number/KPCPTHX36PIV6YLOVZS4NKDDTV/events.json","paper":"https://pith.science/paper/KPCPTHX3"},"agent_actions":{"view_html":"https://pith.science/pith/KPCPTHX36PIV6YLOVZS4NKDDTV","download_json":"https://pith.science/pith/KPCPTHX36PIV6YLOVZS4NKDDTV.json","view_paper":"https://pith.science/paper/KPCPTHX3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.2141&json=true","fetch_graph":"https://pith.science/api/pith-number/KPCPTHX36PIV6YLOVZS4NKDDTV/graph.json","fetch_events":"https://pith.science/api/pith-number/KPCPTHX36PIV6YLOVZS4NKDDTV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KPCPTHX36PIV6YLOVZS4NKDDTV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KPCPTHX36PIV6YLOVZS4NKDDTV/action/storage_attestation","attest_author":"https://pith.science/pith/KPCPTHX36PIV6YLOVZS4NKDDTV/action/author_attestation","sign_citation":"https://pith.science/pith/KPCPTHX36PIV6YLOVZS4NKDDTV/action/citation_signature","submit_replication":"https://pith.science/pith/KPCPTHX36PIV6YLOVZS4NKDDTV/action/replication_record"}},"created_at":"2026-05-18T03:08:24.562424+00:00","updated_at":"2026-05-18T03:08:24.562424+00:00"}