{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:OW5VWAZEO2AYROSSBBJKR2MD5D","short_pith_number":"pith:OW5VWAZE","schema_version":"1.0","canonical_sha256":"75bb5b0324768188ba520852a8e983e8f4053564b9eb318720b61db50edb024f","source":{"kind":"arxiv","id":"1510.02977","version":1},"attestation_state":"computed","paper":{"title":"Boundary layers and incompressible Navier-Stokes-Fourier limit of the Boltzmann Equation in Bounded Domain (I)","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Nader Masmoudi, Ning Jiang","submitted_at":"2015-10-10T20:56:14Z","abstract_excerpt":"We establish the incompressible Navier-Stokes-Fourier limit for solutions to the Boltzmann equation with a general cut-off collision kernel in a bounded domain. Appropriately scaled families of DiPerna-Lions-(Mischler) renormalized solutions with Maxwell reflection boundary conditions are shown to have fluctuations that converge as the Knudsen number goes to zero. Every limit point is a weak solution to the Navier-Stokes-Fourier system with different types of boundary conditions depending on the ratio between the accommodation coefficient and the Knudsen number. The main new result of the pape"},"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":"1510.02977","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2015-10-10T20:56:14Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"5fa9b5978fb162db749077e00cddf99e3129b261d908d6b671d2240858fb706e","abstract_canon_sha256":"89a93358392576b5d72eb14af4ce11aef56fa427a26b23061e99f8fd56e92585"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:33.110859Z","signature_b64":"0AnNOMGo8Oni28zZIm5Xp+8NlodAdJnhbIgLJxwKHOwSnWNkMzVS1Ka0oTVEtISS4jFdl//VEicNHQywbGjvBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"75bb5b0324768188ba520852a8e983e8f4053564b9eb318720b61db50edb024f","last_reissued_at":"2026-05-18T01:30:33.110192Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:33.110192Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Boundary layers and incompressible Navier-Stokes-Fourier limit of the Boltzmann Equation in Bounded Domain (I)","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Nader Masmoudi, Ning Jiang","submitted_at":"2015-10-10T20:56:14Z","abstract_excerpt":"We establish the incompressible Navier-Stokes-Fourier limit for solutions to the Boltzmann equation with a general cut-off collision kernel in a bounded domain. Appropriately scaled families of DiPerna-Lions-(Mischler) renormalized solutions with Maxwell reflection boundary conditions are shown to have fluctuations that converge as the Knudsen number goes to zero. Every limit point is a weak solution to the Navier-Stokes-Fourier system with different types of boundary conditions depending on the ratio between the accommodation coefficient and the Knudsen number. The main new result of the pape"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.02977","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":"1510.02977","created_at":"2026-05-18T01:30:33.110301+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.02977v1","created_at":"2026-05-18T01:30:33.110301+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.02977","created_at":"2026-05-18T01:30:33.110301+00:00"},{"alias_kind":"pith_short_12","alias_value":"OW5VWAZEO2AY","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_16","alias_value":"OW5VWAZEO2AYROSS","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_8","alias_value":"OW5VWAZE","created_at":"2026-05-18T12:29:34.919912+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/OW5VWAZEO2AYROSSBBJKR2MD5D","json":"https://pith.science/pith/OW5VWAZEO2AYROSSBBJKR2MD5D.json","graph_json":"https://pith.science/api/pith-number/OW5VWAZEO2AYROSSBBJKR2MD5D/graph.json","events_json":"https://pith.science/api/pith-number/OW5VWAZEO2AYROSSBBJKR2MD5D/events.json","paper":"https://pith.science/paper/OW5VWAZE"},"agent_actions":{"view_html":"https://pith.science/pith/OW5VWAZEO2AYROSSBBJKR2MD5D","download_json":"https://pith.science/pith/OW5VWAZEO2AYROSSBBJKR2MD5D.json","view_paper":"https://pith.science/paper/OW5VWAZE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.02977&json=true","fetch_graph":"https://pith.science/api/pith-number/OW5VWAZEO2AYROSSBBJKR2MD5D/graph.json","fetch_events":"https://pith.science/api/pith-number/OW5VWAZEO2AYROSSBBJKR2MD5D/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OW5VWAZEO2AYROSSBBJKR2MD5D/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OW5VWAZEO2AYROSSBBJKR2MD5D/action/storage_attestation","attest_author":"https://pith.science/pith/OW5VWAZEO2AYROSSBBJKR2MD5D/action/author_attestation","sign_citation":"https://pith.science/pith/OW5VWAZEO2AYROSSBBJKR2MD5D/action/citation_signature","submit_replication":"https://pith.science/pith/OW5VWAZEO2AYROSSBBJKR2MD5D/action/replication_record"}},"created_at":"2026-05-18T01:30:33.110301+00:00","updated_at":"2026-05-18T01:30:33.110301+00:00"}