{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:DTXFQW25QS4GGU5WCHA63SRT4J","short_pith_number":"pith:DTXFQW25","schema_version":"1.0","canonical_sha256":"1cee585b5d84b86353b611c1edca33e25cdbedc608f3b8bffc41fec8e6cb8c0a","source":{"kind":"arxiv","id":"2111.04016","version":1},"attestation_state":"computed","paper":{"title":"Higher regularity and asymptotic behavior of 2D magnetic Prandtl model in the Prandtl-Hartmann regime","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jincheng Gao, Minling Li, Zheng-an Yao","submitted_at":"2021-11-07T07:00:40Z","abstract_excerpt":"In this paper, we investigate the higher regularity and asymptotic behavior for the 2-D magnetic Prandtl model in the Prandtl-Hartmann regime. Due to the degeneracy of horizontal velocity near boundary, the higher regularity of solution is a tricky problem. By constructing suitable approximated system and establishing closed energy estimate for a good quantity(called \"quotient\" in \\cite{Guo-Iyer-2021}), our first result is to solve this higher regularity problem. Furthermore, we show the global well-posedness and global-in-$x$ asymptotic behavior when the initial data are small perturbation of"},"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":"2111.04016","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2021-11-07T07:00:40Z","cross_cats_sorted":[],"title_canon_sha256":"da6a03665ac7baf8a5770c28057bcaf59a1194ae0f4daffd512c2f667f3aeabe","abstract_canon_sha256":"a63bf65ed43bfc2801642f2d8a616973cb9651aba0a5700a9df693e76741213e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:29:54.711810Z","signature_b64":"YNw5lq3j3F0p/hWe5CdB0Q92sVtZUELW5VuOy2gXt43syhteXQ8poNsZxOZfwIrG0Ofd7RIOR7iARWazbheRBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1cee585b5d84b86353b611c1edca33e25cdbedc608f3b8bffc41fec8e6cb8c0a","last_reissued_at":"2026-07-05T03:29:54.711384Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:29:54.711384Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Higher regularity and asymptotic behavior of 2D magnetic Prandtl model in the Prandtl-Hartmann regime","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jincheng Gao, Minling Li, Zheng-an Yao","submitted_at":"2021-11-07T07:00:40Z","abstract_excerpt":"In this paper, we investigate the higher regularity and asymptotic behavior for the 2-D magnetic Prandtl model in the Prandtl-Hartmann regime. Due to the degeneracy of horizontal velocity near boundary, the higher regularity of solution is a tricky problem. By constructing suitable approximated system and establishing closed energy estimate for a good quantity(called \"quotient\" in \\cite{Guo-Iyer-2021}), our first result is to solve this higher regularity problem. Furthermore, we show the global well-posedness and global-in-$x$ asymptotic behavior when the initial data are small perturbation of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.04016","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/2111.04016/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":"2111.04016","created_at":"2026-07-05T03:29:54.711453+00:00"},{"alias_kind":"arxiv_version","alias_value":"2111.04016v1","created_at":"2026-07-05T03:29:54.711453+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2111.04016","created_at":"2026-07-05T03:29:54.711453+00:00"},{"alias_kind":"pith_short_12","alias_value":"DTXFQW25QS4G","created_at":"2026-07-05T03:29:54.711453+00:00"},{"alias_kind":"pith_short_16","alias_value":"DTXFQW25QS4GGU5W","created_at":"2026-07-05T03:29:54.711453+00:00"},{"alias_kind":"pith_short_8","alias_value":"DTXFQW25","created_at":"2026-07-05T03:29:54.711453+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2411.14081","citing_title":"Prandtl Equations and Related Boundary Layer Equations","ref_index":37,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DTXFQW25QS4GGU5WCHA63SRT4J","json":"https://pith.science/pith/DTXFQW25QS4GGU5WCHA63SRT4J.json","graph_json":"https://pith.science/api/pith-number/DTXFQW25QS4GGU5WCHA63SRT4J/graph.json","events_json":"https://pith.science/api/pith-number/DTXFQW25QS4GGU5WCHA63SRT4J/events.json","paper":"https://pith.science/paper/DTXFQW25"},"agent_actions":{"view_html":"https://pith.science/pith/DTXFQW25QS4GGU5WCHA63SRT4J","download_json":"https://pith.science/pith/DTXFQW25QS4GGU5WCHA63SRT4J.json","view_paper":"https://pith.science/paper/DTXFQW25","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2111.04016&json=true","fetch_graph":"https://pith.science/api/pith-number/DTXFQW25QS4GGU5WCHA63SRT4J/graph.json","fetch_events":"https://pith.science/api/pith-number/DTXFQW25QS4GGU5WCHA63SRT4J/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DTXFQW25QS4GGU5WCHA63SRT4J/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DTXFQW25QS4GGU5WCHA63SRT4J/action/storage_attestation","attest_author":"https://pith.science/pith/DTXFQW25QS4GGU5WCHA63SRT4J/action/author_attestation","sign_citation":"https://pith.science/pith/DTXFQW25QS4GGU5WCHA63SRT4J/action/citation_signature","submit_replication":"https://pith.science/pith/DTXFQW25QS4GGU5WCHA63SRT4J/action/replication_record"}},"created_at":"2026-07-05T03:29:54.711453+00:00","updated_at":"2026-07-05T03:29:54.711453+00:00"}