{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:4DZKECPHNVGBAXFM77XEEONYJU","short_pith_number":"pith:4DZKECPH","schema_version":"1.0","canonical_sha256":"e0f2a209e76d4c105cacffee4239b84d050956944b3d29c8d1e0986ef0e1721e","source":{"kind":"arxiv","id":"2409.08457","version":1},"attestation_state":"computed","paper":{"title":"$\\mathcal R$-bounded operator families arising from a compressible fluid model of Korteweg type with surface tension in the half-space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Miho Murata, Sri Maryani","submitted_at":"2024-09-13T01:07:52Z","abstract_excerpt":"In this paper, we consider a resolvent problem arising from the free boundary value problem for the compressible fluid model of Korteweg type, which is called as the Navier-Stokes-Korteweg system, with surface tension in the half-space. The Navier-Stokes-Korteweg system is known as a diffuse interface model for liquid-vapor two-phase flows. Our purpose is to show the $\\mathcal R$-boundedness for the solution operator families of the resolvent problem, which gives us the maximal regularity estimates in the $L_p$-in-time and $L_q$-in-space setting by applying the Weis's operator valued Fourier m"},"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":"2409.08457","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-09-13T01:07:52Z","cross_cats_sorted":[],"title_canon_sha256":"5933c3b34d6d7f1c6badd8ed842cdaa84cb50f6c9f08be2714ce59b79832487d","abstract_canon_sha256":"2f941574238e7a5efd7d9a271c0f2b49779a856e9147509d29725b474659e6f8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:06:31.582877Z","signature_b64":"SOwYV0yxq28QNWWcknuuV9boeWkcozBTY6Z1ZUCPEesay1C5OoTrxKseoTIMWWdlNgIbXO7aPVvc9LtqcKn4CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e0f2a209e76d4c105cacffee4239b84d050956944b3d29c8d1e0986ef0e1721e","last_reissued_at":"2026-07-05T09:06:31.582349Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:06:31.582349Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$\\mathcal R$-bounded operator families arising from a compressible fluid model of Korteweg type with surface tension in the half-space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Miho Murata, Sri Maryani","submitted_at":"2024-09-13T01:07:52Z","abstract_excerpt":"In this paper, we consider a resolvent problem arising from the free boundary value problem for the compressible fluid model of Korteweg type, which is called as the Navier-Stokes-Korteweg system, with surface tension in the half-space. The Navier-Stokes-Korteweg system is known as a diffuse interface model for liquid-vapor two-phase flows. Our purpose is to show the $\\mathcal R$-boundedness for the solution operator families of the resolvent problem, which gives us the maximal regularity estimates in the $L_p$-in-time and $L_q$-in-space setting by applying the Weis's operator valued Fourier m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.08457","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/2409.08457/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":"2409.08457","created_at":"2026-07-05T09:06:31.582395+00:00"},{"alias_kind":"arxiv_version","alias_value":"2409.08457v1","created_at":"2026-07-05T09:06:31.582395+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.08457","created_at":"2026-07-05T09:06:31.582395+00:00"},{"alias_kind":"pith_short_12","alias_value":"4DZKECPHNVGB","created_at":"2026-07-05T09:06:31.582395+00:00"},{"alias_kind":"pith_short_16","alias_value":"4DZKECPHNVGBAXFM","created_at":"2026-07-05T09:06:31.582395+00:00"},{"alias_kind":"pith_short_8","alias_value":"4DZKECPH","created_at":"2026-07-05T09:06:31.582395+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/4DZKECPHNVGBAXFM77XEEONYJU","json":"https://pith.science/pith/4DZKECPHNVGBAXFM77XEEONYJU.json","graph_json":"https://pith.science/api/pith-number/4DZKECPHNVGBAXFM77XEEONYJU/graph.json","events_json":"https://pith.science/api/pith-number/4DZKECPHNVGBAXFM77XEEONYJU/events.json","paper":"https://pith.science/paper/4DZKECPH"},"agent_actions":{"view_html":"https://pith.science/pith/4DZKECPHNVGBAXFM77XEEONYJU","download_json":"https://pith.science/pith/4DZKECPHNVGBAXFM77XEEONYJU.json","view_paper":"https://pith.science/paper/4DZKECPH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2409.08457&json=true","fetch_graph":"https://pith.science/api/pith-number/4DZKECPHNVGBAXFM77XEEONYJU/graph.json","fetch_events":"https://pith.science/api/pith-number/4DZKECPHNVGBAXFM77XEEONYJU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4DZKECPHNVGBAXFM77XEEONYJU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4DZKECPHNVGBAXFM77XEEONYJU/action/storage_attestation","attest_author":"https://pith.science/pith/4DZKECPHNVGBAXFM77XEEONYJU/action/author_attestation","sign_citation":"https://pith.science/pith/4DZKECPHNVGBAXFM77XEEONYJU/action/citation_signature","submit_replication":"https://pith.science/pith/4DZKECPHNVGBAXFM77XEEONYJU/action/replication_record"}},"created_at":"2026-07-05T09:06:31.582395+00:00","updated_at":"2026-07-05T09:06:31.582395+00:00"}