{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:FZGS72QXAJU6TRT4HSIN2UDKL2","short_pith_number":"pith:FZGS72QX","schema_version":"1.0","canonical_sha256":"2e4d2fea170269e9c67c3c90dd506a5e8b2677aad92add46e08f5f2c37926b2b","source":{"kind":"arxiv","id":"1101.3685","version":1},"attestation_state":"computed","paper":{"title":"Subsonic Flows in a Multi-Dimensional Nozzle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Lili Du, Wei Yan, Zhouping Xin","submitted_at":"2011-01-19T13:43:43Z","abstract_excerpt":"In this paper, we study the global subsonic irrotational flows in a multi-dimensional ($n\\geq 2$) infinitely long nozzle with variable cross sections. The flow is described by the inviscid potential equation, which is a second order quasilinear elliptic equation when the flow is subsonic. First, we prove the existence of the global uniformly subsonic flow in a general infinitely long nozzle for arbitrary dimension for sufficiently small incoming mass flux and obtain the uniqueness of the global uniformly subsonic flow. Furthermore, we show that there exists a critical value of the incoming mas"},"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":"1101.3685","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-01-19T13:43:43Z","cross_cats_sorted":[],"title_canon_sha256":"a6fe918999b7a65292bf51aec8b5af4f9e5913a77107969d0ae724cb55f82228","abstract_canon_sha256":"cafb4370754b97c51faff2466a5e1729999136b4ce9489dbebac9f09d4b9469d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:03:26.398650Z","signature_b64":"b0vmtKzs9oJa520+iJs7V7hVmFkZT3XKf8LSrDghvW9U22nYr/UU1MmgnUX+y1UF+WQ+JyATuhfV4PgCHLPLDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e4d2fea170269e9c67c3c90dd506a5e8b2677aad92add46e08f5f2c37926b2b","last_reissued_at":"2026-05-18T02:03:26.398247Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:03:26.398247Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Subsonic Flows in a Multi-Dimensional Nozzle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Lili Du, Wei Yan, Zhouping Xin","submitted_at":"2011-01-19T13:43:43Z","abstract_excerpt":"In this paper, we study the global subsonic irrotational flows in a multi-dimensional ($n\\geq 2$) infinitely long nozzle with variable cross sections. The flow is described by the inviscid potential equation, which is a second order quasilinear elliptic equation when the flow is subsonic. First, we prove the existence of the global uniformly subsonic flow in a general infinitely long nozzle for arbitrary dimension for sufficiently small incoming mass flux and obtain the uniqueness of the global uniformly subsonic flow. Furthermore, we show that there exists a critical value of the incoming mas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3685","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":"1101.3685","created_at":"2026-05-18T02:03:26.398331+00:00"},{"alias_kind":"arxiv_version","alias_value":"1101.3685v1","created_at":"2026-05-18T02:03:26.398331+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.3685","created_at":"2026-05-18T02:03:26.398331+00:00"},{"alias_kind":"pith_short_12","alias_value":"FZGS72QXAJU6","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_16","alias_value":"FZGS72QXAJU6TRT4","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_8","alias_value":"FZGS72QX","created_at":"2026-05-18T12:26:28.662955+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/FZGS72QXAJU6TRT4HSIN2UDKL2","json":"https://pith.science/pith/FZGS72QXAJU6TRT4HSIN2UDKL2.json","graph_json":"https://pith.science/api/pith-number/FZGS72QXAJU6TRT4HSIN2UDKL2/graph.json","events_json":"https://pith.science/api/pith-number/FZGS72QXAJU6TRT4HSIN2UDKL2/events.json","paper":"https://pith.science/paper/FZGS72QX"},"agent_actions":{"view_html":"https://pith.science/pith/FZGS72QXAJU6TRT4HSIN2UDKL2","download_json":"https://pith.science/pith/FZGS72QXAJU6TRT4HSIN2UDKL2.json","view_paper":"https://pith.science/paper/FZGS72QX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1101.3685&json=true","fetch_graph":"https://pith.science/api/pith-number/FZGS72QXAJU6TRT4HSIN2UDKL2/graph.json","fetch_events":"https://pith.science/api/pith-number/FZGS72QXAJU6TRT4HSIN2UDKL2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FZGS72QXAJU6TRT4HSIN2UDKL2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FZGS72QXAJU6TRT4HSIN2UDKL2/action/storage_attestation","attest_author":"https://pith.science/pith/FZGS72QXAJU6TRT4HSIN2UDKL2/action/author_attestation","sign_citation":"https://pith.science/pith/FZGS72QXAJU6TRT4HSIN2UDKL2/action/citation_signature","submit_replication":"https://pith.science/pith/FZGS72QXAJU6TRT4HSIN2UDKL2/action/replication_record"}},"created_at":"2026-05-18T02:03:26.398331+00:00","updated_at":"2026-05-18T02:03:26.398331+00:00"}