{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:WN4T5YDE75BLL6QLCKCUDGMYKH","short_pith_number":"pith:WN4T5YDE","schema_version":"1.0","canonical_sha256":"b3793ee064ff42b5fa0b128541999851e921b72a2bc0ae77cb9fd8247cfc43a3","source":{"kind":"arxiv","id":"2002.03372","version":1},"attestation_state":"computed","paper":{"title":"Entropy-bounded solutions to the one-dimensional heat conductive compressible Navier-Stokes equations with far field vacuum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Jinkai Li, Zhouping Xin","submitted_at":"2020-02-09T14:28:04Z","abstract_excerpt":"In the presence of vacuum, the physical entropy for polytropic gases behaves singularly and it is thus a challenge to study its dynamics. It is shown in this paper that the boundedness of the entropy can be propagated up to any finite time provided that the initial vacuum presents only at far fields with sufficiently slow decay of the initial density. More precisely, for the Cauchy problem of the one dimensional heat conductive compressible Navier-Stokes equations, the global well-posedness of strong solutions and uniform boundedness of the corresponding entropy are established, as long as 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":"2002.03372","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-02-09T14:28:04Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"2b46b16a709458693bd859368ff8fb0edcb3397054c5196f0148a6591cb6244b","abstract_canon_sha256":"7207ddd49115e0093d054fc87dfe2a6403e41ea368bd1bdcfaca84b208656748"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:39:21.584729Z","signature_b64":"Xz4+tmfvI5lg6bGLMuYxQRS5ouuF+q+OAxdncmOzpN5b4GXAWb7lOnbuXwh03pRanDkuX/qUCAhGBRPZxk4zBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b3793ee064ff42b5fa0b128541999851e921b72a2bc0ae77cb9fd8247cfc43a3","last_reissued_at":"2026-07-05T00:39:21.584302Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:39:21.584302Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Entropy-bounded solutions to the one-dimensional heat conductive compressible Navier-Stokes equations with far field vacuum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Jinkai Li, Zhouping Xin","submitted_at":"2020-02-09T14:28:04Z","abstract_excerpt":"In the presence of vacuum, the physical entropy for polytropic gases behaves singularly and it is thus a challenge to study its dynamics. It is shown in this paper that the boundedness of the entropy can be propagated up to any finite time provided that the initial vacuum presents only at far fields with sufficiently slow decay of the initial density. More precisely, for the Cauchy problem of the one dimensional heat conductive compressible Navier-Stokes equations, the global well-posedness of strong solutions and uniform boundedness of the corresponding entropy are established, as long as the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.03372","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2002.03372/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2002.03372","created_at":"2026-07-05T00:39:21.584368+00:00"},{"alias_kind":"arxiv_version","alias_value":"2002.03372v1","created_at":"2026-07-05T00:39:21.584368+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2002.03372","created_at":"2026-07-05T00:39:21.584368+00:00"},{"alias_kind":"pith_short_12","alias_value":"WN4T5YDE75BL","created_at":"2026-07-05T00:39:21.584368+00:00"},{"alias_kind":"pith_short_16","alias_value":"WN4T5YDE75BLL6QL","created_at":"2026-07-05T00:39:21.584368+00:00"},{"alias_kind":"pith_short_8","alias_value":"WN4T5YDE","created_at":"2026-07-05T00:39:21.584368+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/WN4T5YDE75BLL6QLCKCUDGMYKH","json":"https://pith.science/pith/WN4T5YDE75BLL6QLCKCUDGMYKH.json","graph_json":"https://pith.science/api/pith-number/WN4T5YDE75BLL6QLCKCUDGMYKH/graph.json","events_json":"https://pith.science/api/pith-number/WN4T5YDE75BLL6QLCKCUDGMYKH/events.json","paper":"https://pith.science/paper/WN4T5YDE"},"agent_actions":{"view_html":"https://pith.science/pith/WN4T5YDE75BLL6QLCKCUDGMYKH","download_json":"https://pith.science/pith/WN4T5YDE75BLL6QLCKCUDGMYKH.json","view_paper":"https://pith.science/paper/WN4T5YDE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2002.03372&json=true","fetch_graph":"https://pith.science/api/pith-number/WN4T5YDE75BLL6QLCKCUDGMYKH/graph.json","fetch_events":"https://pith.science/api/pith-number/WN4T5YDE75BLL6QLCKCUDGMYKH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WN4T5YDE75BLL6QLCKCUDGMYKH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WN4T5YDE75BLL6QLCKCUDGMYKH/action/storage_attestation","attest_author":"https://pith.science/pith/WN4T5YDE75BLL6QLCKCUDGMYKH/action/author_attestation","sign_citation":"https://pith.science/pith/WN4T5YDE75BLL6QLCKCUDGMYKH/action/citation_signature","submit_replication":"https://pith.science/pith/WN4T5YDE75BLL6QLCKCUDGMYKH/action/replication_record"}},"created_at":"2026-07-05T00:39:21.584368+00:00","updated_at":"2026-07-05T00:39:21.584368+00:00"}