{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:LILSUAOULJIUBBEWQQ6T2UE7BM","short_pith_number":"pith:LILSUAOU","schema_version":"1.0","canonical_sha256":"5a172a01d45a51408496843d3d509f0b1b88c1a676aacbec79cd212c6de567e5","source":{"kind":"arxiv","id":"1305.6296","version":2},"attestation_state":"computed","paper":{"title":"Derivation of a viscous Boussinesq system for surface water waves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Herv\\'e Le Meur (LM-Orsay)","submitted_at":"2013-05-27T19:09:13Z","abstract_excerpt":"In this article, we derive a viscous Boussinesq system for surface water waves from Navier-Stokes equations. We use neither the irrotationality assumption, nor the Zakharov-Craig-Sulem formulation. During the derivation, we find the bottom shear stress, and also the decay rate for shallow water. In order to justify our derivation, we derive the viscous Korteweg-de Vries equation from our viscous Boussinesq system and compare it to the ones found in the bibliography. We also extend the system to the 3-D case."},"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":"1305.6296","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-27T19:09:13Z","cross_cats_sorted":[],"title_canon_sha256":"081642e878bd1b36ef11155726cb85f461bf01ef05317b6635715af4cd0f08de","abstract_canon_sha256":"587ac12e2fb749e74554aa773bae5b380cf243d60ee6a77d7773c627d0bf0b9b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:33.936158Z","signature_b64":"iRONDrH7ltH65p4XnwRgIrS1+j/cBGC9BTzFGvwgGVu760BRrmCqFWfAOCrVR+oQYydAtHg+c4XYj/inkIMdCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5a172a01d45a51408496843d3d509f0b1b88c1a676aacbec79cd212c6de567e5","last_reissued_at":"2026-05-18T02:30:33.935622Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:33.935622Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Derivation of a viscous Boussinesq system for surface water waves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Herv\\'e Le Meur (LM-Orsay)","submitted_at":"2013-05-27T19:09:13Z","abstract_excerpt":"In this article, we derive a viscous Boussinesq system for surface water waves from Navier-Stokes equations. We use neither the irrotationality assumption, nor the Zakharov-Craig-Sulem formulation. During the derivation, we find the bottom shear stress, and also the decay rate for shallow water. In order to justify our derivation, we derive the viscous Korteweg-de Vries equation from our viscous Boussinesq system and compare it to the ones found in the bibliography. We also extend the system to the 3-D case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6296","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":"1305.6296","created_at":"2026-05-18T02:30:33.935710+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.6296v2","created_at":"2026-05-18T02:30:33.935710+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.6296","created_at":"2026-05-18T02:30:33.935710+00:00"},{"alias_kind":"pith_short_12","alias_value":"LILSUAOULJIU","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_16","alias_value":"LILSUAOULJIUBBEW","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_8","alias_value":"LILSUAOU","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/LILSUAOULJIUBBEWQQ6T2UE7BM","json":"https://pith.science/pith/LILSUAOULJIUBBEWQQ6T2UE7BM.json","graph_json":"https://pith.science/api/pith-number/LILSUAOULJIUBBEWQQ6T2UE7BM/graph.json","events_json":"https://pith.science/api/pith-number/LILSUAOULJIUBBEWQQ6T2UE7BM/events.json","paper":"https://pith.science/paper/LILSUAOU"},"agent_actions":{"view_html":"https://pith.science/pith/LILSUAOULJIUBBEWQQ6T2UE7BM","download_json":"https://pith.science/pith/LILSUAOULJIUBBEWQQ6T2UE7BM.json","view_paper":"https://pith.science/paper/LILSUAOU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.6296&json=true","fetch_graph":"https://pith.science/api/pith-number/LILSUAOULJIUBBEWQQ6T2UE7BM/graph.json","fetch_events":"https://pith.science/api/pith-number/LILSUAOULJIUBBEWQQ6T2UE7BM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LILSUAOULJIUBBEWQQ6T2UE7BM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LILSUAOULJIUBBEWQQ6T2UE7BM/action/storage_attestation","attest_author":"https://pith.science/pith/LILSUAOULJIUBBEWQQ6T2UE7BM/action/author_attestation","sign_citation":"https://pith.science/pith/LILSUAOULJIUBBEWQQ6T2UE7BM/action/citation_signature","submit_replication":"https://pith.science/pith/LILSUAOULJIUBBEWQQ6T2UE7BM/action/replication_record"}},"created_at":"2026-05-18T02:30:33.935710+00:00","updated_at":"2026-05-18T02:30:33.935710+00:00"}