{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:HDEKRA3FTADMIAJA2DKYQXNY7I","short_pith_number":"pith:HDEKRA3F","schema_version":"1.0","canonical_sha256":"38c8a883659806c40120d0d5885db8fa1d96af4624e64851304ff4f41a9a07c5","source":{"kind":"arxiv","id":"1302.7084","version":1},"attestation_state":"computed","paper":{"title":"Ill-posedness of the incompressible Navier-Stokes equations in $\\dot{F}^{-1,q}_{\\infty}({R}^3)$","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"C. Deng, X. Yao","submitted_at":"2013-02-28T05:00:58Z","abstract_excerpt":"In this paper, authors show the ill-posedness of 3D incompressible Navier-Stokes equations in the critical Triebel-Lizorkin spaces $ \\dot{F}^{-1,q}_{\\infty} (\\mathbb{R}^3) $ for any $ q>2 $ in the sense that arbitrarily small initial data of $ \\dot{F}^{-1,q}_{\\infty}(\\mathbb{R}^3) $ can lead the corresponding solution to become arbitrarily large after an arbitrarily short time. In view of the well-posedness of 3D-incompressible Navier-Stokes equations in $ BMO^{-1} $ (i.e. the Triebel-Lizorkin space $ \\dot{F}^{-1,2}_{\\infty}(\\mathbb{R}^3) $) by Koch and Tataru, our work completes a dichotomy o"},"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":"1302.7084","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.AP","submitted_at":"2013-02-28T05:00:58Z","cross_cats_sorted":[],"title_canon_sha256":"6bf56a972f43f036d75e93386cc6e89e1ae4bef749c541d20b10435b5848493e","abstract_canon_sha256":"11f977dfedbb1aefef9379d5e5285b1d5e0738bb72619dc512ca54b63134fd9a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:32:17.523795Z","signature_b64":"BCmWozaeGM2slaTYJhZk1e8Qqiy0yqWAbJMw/lF8m3HX/LFJZ5hGXacT2m7rZ6jIAfvz6ap1upzU0v6BkJLcAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"38c8a883659806c40120d0d5885db8fa1d96af4624e64851304ff4f41a9a07c5","last_reissued_at":"2026-05-18T03:32:17.522989Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:32:17.522989Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ill-posedness of the incompressible Navier-Stokes equations in $\\dot{F}^{-1,q}_{\\infty}({R}^3)$","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"C. Deng, X. Yao","submitted_at":"2013-02-28T05:00:58Z","abstract_excerpt":"In this paper, authors show the ill-posedness of 3D incompressible Navier-Stokes equations in the critical Triebel-Lizorkin spaces $ \\dot{F}^{-1,q}_{\\infty} (\\mathbb{R}^3) $ for any $ q>2 $ in the sense that arbitrarily small initial data of $ \\dot{F}^{-1,q}_{\\infty}(\\mathbb{R}^3) $ can lead the corresponding solution to become arbitrarily large after an arbitrarily short time. In view of the well-posedness of 3D-incompressible Navier-Stokes equations in $ BMO^{-1} $ (i.e. the Triebel-Lizorkin space $ \\dot{F}^{-1,2}_{\\infty}(\\mathbb{R}^3) $) by Koch and Tataru, our work completes a dichotomy o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.7084","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":"1302.7084","created_at":"2026-05-18T03:32:17.523130+00:00"},{"alias_kind":"arxiv_version","alias_value":"1302.7084v1","created_at":"2026-05-18T03:32:17.523130+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.7084","created_at":"2026-05-18T03:32:17.523130+00:00"},{"alias_kind":"pith_short_12","alias_value":"HDEKRA3FTADM","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_16","alias_value":"HDEKRA3FTADMIAJA","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_8","alias_value":"HDEKRA3F","created_at":"2026-05-18T12:27:46.883200+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/HDEKRA3FTADMIAJA2DKYQXNY7I","json":"https://pith.science/pith/HDEKRA3FTADMIAJA2DKYQXNY7I.json","graph_json":"https://pith.science/api/pith-number/HDEKRA3FTADMIAJA2DKYQXNY7I/graph.json","events_json":"https://pith.science/api/pith-number/HDEKRA3FTADMIAJA2DKYQXNY7I/events.json","paper":"https://pith.science/paper/HDEKRA3F"},"agent_actions":{"view_html":"https://pith.science/pith/HDEKRA3FTADMIAJA2DKYQXNY7I","download_json":"https://pith.science/pith/HDEKRA3FTADMIAJA2DKYQXNY7I.json","view_paper":"https://pith.science/paper/HDEKRA3F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1302.7084&json=true","fetch_graph":"https://pith.science/api/pith-number/HDEKRA3FTADMIAJA2DKYQXNY7I/graph.json","fetch_events":"https://pith.science/api/pith-number/HDEKRA3FTADMIAJA2DKYQXNY7I/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HDEKRA3FTADMIAJA2DKYQXNY7I/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HDEKRA3FTADMIAJA2DKYQXNY7I/action/storage_attestation","attest_author":"https://pith.science/pith/HDEKRA3FTADMIAJA2DKYQXNY7I/action/author_attestation","sign_citation":"https://pith.science/pith/HDEKRA3FTADMIAJA2DKYQXNY7I/action/citation_signature","submit_replication":"https://pith.science/pith/HDEKRA3FTADMIAJA2DKYQXNY7I/action/replication_record"}},"created_at":"2026-05-18T03:32:17.523130+00:00","updated_at":"2026-05-18T03:32:17.523130+00:00"}