{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:JC6MIHVJHJGSA3W5NC4UJE26ZB","short_pith_number":"pith:JC6MIHVJ","schema_version":"1.0","canonical_sha256":"48bcc41ea93a4d206edd68b944935ec873dce02dcf8ddd91f6a6b949b6083b9f","source":{"kind":"arxiv","id":"1611.06077","version":1},"attestation_state":"computed","paper":{"title":"Lp estimates for the homogenization of stokes problem in a perforated domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Amina Mecherbet (UM, IMAG), Matthieu Hillairet (IMAG, UM)","submitted_at":"2016-11-18T13:58:42Z","abstract_excerpt":"In this paper, we consider the Stokes equations in a perforated domain. When the number of holes increases while their radius tends to 0, it is proven in [L. Desvillettes, F. Golse and V. Ricci. The mean field limit for solid particles in a Navier-Stokes flow. J. Stat. Phys. 131: 941-967, 2008], under suitable dilution assumptions, that the solution is well-approximated asymptotically by solving a Stokes-Brinkman equation. We provide here quantitative estimates in L p-norms of this convergence."},"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":"1611.06077","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-11-18T13:58:42Z","cross_cats_sorted":[],"title_canon_sha256":"e4e5d2ffbf6bd5779aa810444b24e8396e5d79141292df91875f0cb26d0875d1","abstract_canon_sha256":"33e12b5af3b8460e0fd46b792ae24c63fd1628c8c8cc731b24ddc29383d97f5d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:43.152476Z","signature_b64":"Ti2df2VA/ITbYea0V2UB0+9lmym63X3dfGzsxrJ1OKvBqNOMbs8c4tiJ2oJANTpRZJVER5VKsJ8jA/ZIpsr3Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"48bcc41ea93a4d206edd68b944935ec873dce02dcf8ddd91f6a6b949b6083b9f","last_reissued_at":"2026-05-18T00:57:43.151923Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:43.151923Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lp estimates for the homogenization of stokes problem in a perforated domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Amina Mecherbet (UM, IMAG), Matthieu Hillairet (IMAG, UM)","submitted_at":"2016-11-18T13:58:42Z","abstract_excerpt":"In this paper, we consider the Stokes equations in a perforated domain. When the number of holes increases while their radius tends to 0, it is proven in [L. Desvillettes, F. Golse and V. Ricci. The mean field limit for solid particles in a Navier-Stokes flow. J. Stat. Phys. 131: 941-967, 2008], under suitable dilution assumptions, that the solution is well-approximated asymptotically by solving a Stokes-Brinkman equation. We provide here quantitative estimates in L p-norms of this convergence."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.06077","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":"1611.06077","created_at":"2026-05-18T00:57:43.151999+00:00"},{"alias_kind":"arxiv_version","alias_value":"1611.06077v1","created_at":"2026-05-18T00:57:43.151999+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.06077","created_at":"2026-05-18T00:57:43.151999+00:00"},{"alias_kind":"pith_short_12","alias_value":"JC6MIHVJHJGS","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_16","alias_value":"JC6MIHVJHJGSA3W5","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_8","alias_value":"JC6MIHVJ","created_at":"2026-05-18T12:30:25.849896+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/JC6MIHVJHJGSA3W5NC4UJE26ZB","json":"https://pith.science/pith/JC6MIHVJHJGSA3W5NC4UJE26ZB.json","graph_json":"https://pith.science/api/pith-number/JC6MIHVJHJGSA3W5NC4UJE26ZB/graph.json","events_json":"https://pith.science/api/pith-number/JC6MIHVJHJGSA3W5NC4UJE26ZB/events.json","paper":"https://pith.science/paper/JC6MIHVJ"},"agent_actions":{"view_html":"https://pith.science/pith/JC6MIHVJHJGSA3W5NC4UJE26ZB","download_json":"https://pith.science/pith/JC6MIHVJHJGSA3W5NC4UJE26ZB.json","view_paper":"https://pith.science/paper/JC6MIHVJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1611.06077&json=true","fetch_graph":"https://pith.science/api/pith-number/JC6MIHVJHJGSA3W5NC4UJE26ZB/graph.json","fetch_events":"https://pith.science/api/pith-number/JC6MIHVJHJGSA3W5NC4UJE26ZB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JC6MIHVJHJGSA3W5NC4UJE26ZB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JC6MIHVJHJGSA3W5NC4UJE26ZB/action/storage_attestation","attest_author":"https://pith.science/pith/JC6MIHVJHJGSA3W5NC4UJE26ZB/action/author_attestation","sign_citation":"https://pith.science/pith/JC6MIHVJHJGSA3W5NC4UJE26ZB/action/citation_signature","submit_replication":"https://pith.science/pith/JC6MIHVJHJGSA3W5NC4UJE26ZB/action/replication_record"}},"created_at":"2026-05-18T00:57:43.151999+00:00","updated_at":"2026-05-18T00:57:43.151999+00:00"}