{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:QMBJ4D5SADC6GTWRHYYLU27TIO","short_pith_number":"pith:QMBJ4D5S","schema_version":"1.0","canonical_sha256":"83029e0fb200c5e34ed13e30ba6bf3438bf7c6ec7fcc836d994e160c62beed4f","source":{"kind":"arxiv","id":"1406.3165","version":1},"attestation_state":"computed","paper":{"title":"The primitive equations of the atmosphere in presence of vapor saturation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Aimin Huang, Igor Kukavica, Michele Coti Zelati, Mohammed Ziane, Roger Temam","submitted_at":"2014-06-12T09:34:05Z","abstract_excerpt":"A modification of the classical primitive equations of the atmosphere is considered in order to take into account important phase transition phenomena due to air saturation and condensation. We provide a mathematical formulation of the problem that appears to be new in this setting, by making use of differential inclusions and variational inequalities, and which allows to develop a rather complete theory for the solutions to what turns out to be a nonlinearly coupled system of non-smooth partial differential equations. Specifically we prove global existence of quasi-strong and strong solutions"},"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":"1406.3165","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-06-12T09:34:05Z","cross_cats_sorted":[],"title_canon_sha256":"6185831fa03f1a4681cda36d6224ab37b0227372d66271d3c703b25f81f7817e","abstract_canon_sha256":"34ab784905fb3a3f9a7bebf328da76463f92b4c9d1a4af56e3c4185df63973eb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:42:58.077077Z","signature_b64":"QhPoAN2GecfI2KULg6mWflfotIE8KCKI9YhjyEs1wjA0zptBTqmDTdZtDuPgWhWk45H1wEQ9VsE76iCm8Z5ZAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"83029e0fb200c5e34ed13e30ba6bf3438bf7c6ec7fcc836d994e160c62beed4f","last_reissued_at":"2026-05-18T01:42:58.076548Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:42:58.076548Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The primitive equations of the atmosphere in presence of vapor saturation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Aimin Huang, Igor Kukavica, Michele Coti Zelati, Mohammed Ziane, Roger Temam","submitted_at":"2014-06-12T09:34:05Z","abstract_excerpt":"A modification of the classical primitive equations of the atmosphere is considered in order to take into account important phase transition phenomena due to air saturation and condensation. We provide a mathematical formulation of the problem that appears to be new in this setting, by making use of differential inclusions and variational inequalities, and which allows to develop a rather complete theory for the solutions to what turns out to be a nonlinearly coupled system of non-smooth partial differential equations. Specifically we prove global existence of quasi-strong and strong solutions"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3165","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":"1406.3165","created_at":"2026-05-18T01:42:58.076634+00:00"},{"alias_kind":"arxiv_version","alias_value":"1406.3165v1","created_at":"2026-05-18T01:42:58.076634+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.3165","created_at":"2026-05-18T01:42:58.076634+00:00"},{"alias_kind":"pith_short_12","alias_value":"QMBJ4D5SADC6","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_16","alias_value":"QMBJ4D5SADC6GTWR","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_8","alias_value":"QMBJ4D5S","created_at":"2026-05-18T12:28:46.137349+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/QMBJ4D5SADC6GTWRHYYLU27TIO","json":"https://pith.science/pith/QMBJ4D5SADC6GTWRHYYLU27TIO.json","graph_json":"https://pith.science/api/pith-number/QMBJ4D5SADC6GTWRHYYLU27TIO/graph.json","events_json":"https://pith.science/api/pith-number/QMBJ4D5SADC6GTWRHYYLU27TIO/events.json","paper":"https://pith.science/paper/QMBJ4D5S"},"agent_actions":{"view_html":"https://pith.science/pith/QMBJ4D5SADC6GTWRHYYLU27TIO","download_json":"https://pith.science/pith/QMBJ4D5SADC6GTWRHYYLU27TIO.json","view_paper":"https://pith.science/paper/QMBJ4D5S","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1406.3165&json=true","fetch_graph":"https://pith.science/api/pith-number/QMBJ4D5SADC6GTWRHYYLU27TIO/graph.json","fetch_events":"https://pith.science/api/pith-number/QMBJ4D5SADC6GTWRHYYLU27TIO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QMBJ4D5SADC6GTWRHYYLU27TIO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QMBJ4D5SADC6GTWRHYYLU27TIO/action/storage_attestation","attest_author":"https://pith.science/pith/QMBJ4D5SADC6GTWRHYYLU27TIO/action/author_attestation","sign_citation":"https://pith.science/pith/QMBJ4D5SADC6GTWRHYYLU27TIO/action/citation_signature","submit_replication":"https://pith.science/pith/QMBJ4D5SADC6GTWRHYYLU27TIO/action/replication_record"}},"created_at":"2026-05-18T01:42:58.076634+00:00","updated_at":"2026-05-18T01:42:58.076634+00:00"}