{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:3IIIAEX3YR6L3QNUDV4XOCDPOC","short_pith_number":"pith:3IIIAEX3","schema_version":"1.0","canonical_sha256":"da108012fbc47cbdc1b41d7977086f70bf941651f047e0b4ae74402a22a669e6","source":{"kind":"arxiv","id":"1304.4376","version":1},"attestation_state":"computed","paper":{"title":"The Oberbeck-Boussinesq approximation in critical spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Lingbing He, Rapha\\\"el Danchin (LAMA)","submitted_at":"2013-04-16T09:19:45Z","abstract_excerpt":"In this paper we study the validity of the so-called Oberbeck-Boussinesq approximation for compressible viscous perfect gases in the whole three-dimensional space. Both the cases of uids with positive heat conductivity and zero conductivity are considered. For small perturbations of a constant equilibrium, we establish the global existence of unique strong solutions in a critical regularity functional framework. Next, taking advantage of Strichartz estimates for the associated system of acoustic waves, and of uniform estimates with respect to the Mach number, we obtain all-time convergence to "},"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":"1304.4376","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-16T09:19:45Z","cross_cats_sorted":[],"title_canon_sha256":"6ca0acdd18b9648943cea707adb84333ff050b0ec69d54733c2030d68e3227cd","abstract_canon_sha256":"20071a203b1372d18d8bbc0b5b57adf480b07d82cea47216035294b93b684540"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:53.261157Z","signature_b64":"ENIxNfM9TP1B76H37ts3DIobuw1xn+z5urvJv9Mgb1cyexf6e5y4br99pdO0/BTlfT7rf8nukoe4LiNXwE4LBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da108012fbc47cbdc1b41d7977086f70bf941651f047e0b4ae74402a22a669e6","last_reissued_at":"2026-05-18T03:27:53.260591Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:53.260591Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Oberbeck-Boussinesq approximation in critical spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Lingbing He, Rapha\\\"el Danchin (LAMA)","submitted_at":"2013-04-16T09:19:45Z","abstract_excerpt":"In this paper we study the validity of the so-called Oberbeck-Boussinesq approximation for compressible viscous perfect gases in the whole three-dimensional space. Both the cases of uids with positive heat conductivity and zero conductivity are considered. For small perturbations of a constant equilibrium, we establish the global existence of unique strong solutions in a critical regularity functional framework. Next, taking advantage of Strichartz estimates for the associated system of acoustic waves, and of uniform estimates with respect to the Mach number, we obtain all-time convergence to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.4376","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":"1304.4376","created_at":"2026-05-18T03:27:53.260663+00:00"},{"alias_kind":"arxiv_version","alias_value":"1304.4376v1","created_at":"2026-05-18T03:27:53.260663+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.4376","created_at":"2026-05-18T03:27:53.260663+00:00"},{"alias_kind":"pith_short_12","alias_value":"3IIIAEX3YR6L","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_16","alias_value":"3IIIAEX3YR6L3QNU","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_8","alias_value":"3IIIAEX3","created_at":"2026-05-18T12:27:32.513160+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/3IIIAEX3YR6L3QNUDV4XOCDPOC","json":"https://pith.science/pith/3IIIAEX3YR6L3QNUDV4XOCDPOC.json","graph_json":"https://pith.science/api/pith-number/3IIIAEX3YR6L3QNUDV4XOCDPOC/graph.json","events_json":"https://pith.science/api/pith-number/3IIIAEX3YR6L3QNUDV4XOCDPOC/events.json","paper":"https://pith.science/paper/3IIIAEX3"},"agent_actions":{"view_html":"https://pith.science/pith/3IIIAEX3YR6L3QNUDV4XOCDPOC","download_json":"https://pith.science/pith/3IIIAEX3YR6L3QNUDV4XOCDPOC.json","view_paper":"https://pith.science/paper/3IIIAEX3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1304.4376&json=true","fetch_graph":"https://pith.science/api/pith-number/3IIIAEX3YR6L3QNUDV4XOCDPOC/graph.json","fetch_events":"https://pith.science/api/pith-number/3IIIAEX3YR6L3QNUDV4XOCDPOC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3IIIAEX3YR6L3QNUDV4XOCDPOC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3IIIAEX3YR6L3QNUDV4XOCDPOC/action/storage_attestation","attest_author":"https://pith.science/pith/3IIIAEX3YR6L3QNUDV4XOCDPOC/action/author_attestation","sign_citation":"https://pith.science/pith/3IIIAEX3YR6L3QNUDV4XOCDPOC/action/citation_signature","submit_replication":"https://pith.science/pith/3IIIAEX3YR6L3QNUDV4XOCDPOC/action/replication_record"}},"created_at":"2026-05-18T03:27:53.260663+00:00","updated_at":"2026-05-18T03:27:53.260663+00:00"}