{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:7H3K6BED4KCD4ODEANKLUMCJEM","short_pith_number":"pith:7H3K6BED","schema_version":"1.0","canonical_sha256":"f9f6af0483e2843e38640354ba304923033156d5285412a00ddced01e4d0ec1e","source":{"kind":"arxiv","id":"1701.04144","version":2},"attestation_state":"computed","paper":{"title":"The Boltzmann equation with incoming boundary condition: global solutions and Navier-Stokes limit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ning Jiang, Xu Zhang","submitted_at":"2017-01-16T02:40:27Z","abstract_excerpt":"We consider the Boltzmann equations with cutoff collision kernels in bounded domains. For the initial data with finite physical bounds, we prove the existence of global-in-time renormalized solutions in the sense of DiPerna-Lions endowed with incoming boundary condition. Moreover, we justify the limit as the Knudsen number $\\epsilon\\rightarrow 0$ to Leray solutions of the incompressible Navier-Stokes-Fourier equations with homogeneous Dirichlet conditions from renormalized solutions of the scaled Boltzmann equations when the incoming data are close to the global Maxwellian in the sense of the "},"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":"1701.04144","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-16T02:40:27Z","cross_cats_sorted":[],"title_canon_sha256":"e17af9c07eed85bdfed7492b01d1493aa6b219d84eb9caf8602665522c5d8ece","abstract_canon_sha256":"d9a9dfedb8415d93357e74290eaf7d6bc0dff03996fc0baa106e8ba3d107afe3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:43.725560Z","signature_b64":"x94q2B/4R7HqiEiHjoB/8TRzAjssgt+EextumNmaENKklxlDSCT5vk8ybCTMCfb/XDiPK6Nyi6azqqaG2ZTMDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f9f6af0483e2843e38640354ba304923033156d5285412a00ddced01e4d0ec1e","last_reissued_at":"2026-05-18T00:35:43.724855Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:43.724855Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Boltzmann equation with incoming boundary condition: global solutions and Navier-Stokes limit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ning Jiang, Xu Zhang","submitted_at":"2017-01-16T02:40:27Z","abstract_excerpt":"We consider the Boltzmann equations with cutoff collision kernels in bounded domains. For the initial data with finite physical bounds, we prove the existence of global-in-time renormalized solutions in the sense of DiPerna-Lions endowed with incoming boundary condition. Moreover, we justify the limit as the Knudsen number $\\epsilon\\rightarrow 0$ to Leray solutions of the incompressible Navier-Stokes-Fourier equations with homogeneous Dirichlet conditions from renormalized solutions of the scaled Boltzmann equations when the incoming data are close to the global Maxwellian in the sense of the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.04144","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":"1701.04144","created_at":"2026-05-18T00:35:43.724968+00:00"},{"alias_kind":"arxiv_version","alias_value":"1701.04144v2","created_at":"2026-05-18T00:35:43.724968+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.04144","created_at":"2026-05-18T00:35:43.724968+00:00"},{"alias_kind":"pith_short_12","alias_value":"7H3K6BED4KCD","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_16","alias_value":"7H3K6BED4KCD4ODE","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_8","alias_value":"7H3K6BED","created_at":"2026-05-18T12:31:05.417338+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/7H3K6BED4KCD4ODEANKLUMCJEM","json":"https://pith.science/pith/7H3K6BED4KCD4ODEANKLUMCJEM.json","graph_json":"https://pith.science/api/pith-number/7H3K6BED4KCD4ODEANKLUMCJEM/graph.json","events_json":"https://pith.science/api/pith-number/7H3K6BED4KCD4ODEANKLUMCJEM/events.json","paper":"https://pith.science/paper/7H3K6BED"},"agent_actions":{"view_html":"https://pith.science/pith/7H3K6BED4KCD4ODEANKLUMCJEM","download_json":"https://pith.science/pith/7H3K6BED4KCD4ODEANKLUMCJEM.json","view_paper":"https://pith.science/paper/7H3K6BED","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1701.04144&json=true","fetch_graph":"https://pith.science/api/pith-number/7H3K6BED4KCD4ODEANKLUMCJEM/graph.json","fetch_events":"https://pith.science/api/pith-number/7H3K6BED4KCD4ODEANKLUMCJEM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7H3K6BED4KCD4ODEANKLUMCJEM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7H3K6BED4KCD4ODEANKLUMCJEM/action/storage_attestation","attest_author":"https://pith.science/pith/7H3K6BED4KCD4ODEANKLUMCJEM/action/author_attestation","sign_citation":"https://pith.science/pith/7H3K6BED4KCD4ODEANKLUMCJEM/action/citation_signature","submit_replication":"https://pith.science/pith/7H3K6BED4KCD4ODEANKLUMCJEM/action/replication_record"}},"created_at":"2026-05-18T00:35:43.724968+00:00","updated_at":"2026-05-18T00:35:43.724968+00:00"}