{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:A2YLWE443EGDOBUOCVNHAQVFQS","short_pith_number":"pith:A2YLWE44","schema_version":"1.0","canonical_sha256":"06b0bb139cd90c37068e155a7042a5849f83c36780dbb1a3a304975760ad1a13","source":{"kind":"arxiv","id":"1506.08964","version":2},"attestation_state":"computed","paper":{"title":"Small moving rigid body into a viscous incompressible fluid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Christophe Lacave (IF, IMJ), SPHINX), Tak\\'eo Takahashi (EDP","submitted_at":"2015-06-30T07:00:38Z","abstract_excerpt":"We consider a single disk moving under the influence of a 2D viscous fluid and we study the asymptotic as the size of the solid tends to zero.If the density of the solid is independent of $\\varepsilon$, the energy equality is not sufficient to obtain a uniform estimate for the solid velocity. This will be achieved thanks to the optimal $L^p-L^q$ decay estimates of the semigroup associated to the fluid-rigid body system and to a fixed point argument. Next, we will deduce the convergence to the solution of the Navier-Stokes equations in $\\R^2$."},"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":"1506.08964","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-06-30T07:00:38Z","cross_cats_sorted":[],"title_canon_sha256":"6d5ff2ded7723542105dd74cf2f5a5e346382856b126b064b4119a05e3eea44e","abstract_canon_sha256":"b391a4e8fc05de1cac6821557e6075360ef68098580bde52806c291a66ff3995"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:10.195609Z","signature_b64":"qjoIHeRXgOjZ7gqagfvXgRuWa+1XgIHc+RLIyRnrmaerhnFO9O6AUnim77mLDjgoNvDdmilkxDrfX4fNadSkCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"06b0bb139cd90c37068e155a7042a5849f83c36780dbb1a3a304975760ad1a13","last_reissued_at":"2026-05-18T01:00:10.194788Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:10.194788Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Small moving rigid body into a viscous incompressible fluid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Christophe Lacave (IF, IMJ), SPHINX), Tak\\'eo Takahashi (EDP","submitted_at":"2015-06-30T07:00:38Z","abstract_excerpt":"We consider a single disk moving under the influence of a 2D viscous fluid and we study the asymptotic as the size of the solid tends to zero.If the density of the solid is independent of $\\varepsilon$, the energy equality is not sufficient to obtain a uniform estimate for the solid velocity. This will be achieved thanks to the optimal $L^p-L^q$ decay estimates of the semigroup associated to the fluid-rigid body system and to a fixed point argument. Next, we will deduce the convergence to the solution of the Navier-Stokes equations in $\\R^2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.08964","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":"1506.08964","created_at":"2026-05-18T01:00:10.194930+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.08964v2","created_at":"2026-05-18T01:00:10.194930+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.08964","created_at":"2026-05-18T01:00:10.194930+00:00"},{"alias_kind":"pith_short_12","alias_value":"A2YLWE443EGD","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_16","alias_value":"A2YLWE443EGDOBUO","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_8","alias_value":"A2YLWE44","created_at":"2026-05-18T12:29:10.953037+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/A2YLWE443EGDOBUOCVNHAQVFQS","json":"https://pith.science/pith/A2YLWE443EGDOBUOCVNHAQVFQS.json","graph_json":"https://pith.science/api/pith-number/A2YLWE443EGDOBUOCVNHAQVFQS/graph.json","events_json":"https://pith.science/api/pith-number/A2YLWE443EGDOBUOCVNHAQVFQS/events.json","paper":"https://pith.science/paper/A2YLWE44"},"agent_actions":{"view_html":"https://pith.science/pith/A2YLWE443EGDOBUOCVNHAQVFQS","download_json":"https://pith.science/pith/A2YLWE443EGDOBUOCVNHAQVFQS.json","view_paper":"https://pith.science/paper/A2YLWE44","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.08964&json=true","fetch_graph":"https://pith.science/api/pith-number/A2YLWE443EGDOBUOCVNHAQVFQS/graph.json","fetch_events":"https://pith.science/api/pith-number/A2YLWE443EGDOBUOCVNHAQVFQS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/A2YLWE443EGDOBUOCVNHAQVFQS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/A2YLWE443EGDOBUOCVNHAQVFQS/action/storage_attestation","attest_author":"https://pith.science/pith/A2YLWE443EGDOBUOCVNHAQVFQS/action/author_attestation","sign_citation":"https://pith.science/pith/A2YLWE443EGDOBUOCVNHAQVFQS/action/citation_signature","submit_replication":"https://pith.science/pith/A2YLWE443EGDOBUOCVNHAQVFQS/action/replication_record"}},"created_at":"2026-05-18T01:00:10.194930+00:00","updated_at":"2026-05-18T01:00:10.194930+00:00"}