{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:6652XAOYPVWGHVZXYMHJK76VPU","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"39bcefe06aef5cc9fc246fa56a0b48a06da83498bee91b3fffe7332a00730dd8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-10T01:13:39Z","title_canon_sha256":"32ae026749436bce79b9d49d38aa2af74603ff38a7550301e97c1451906fe077"},"schema_version":"1.0","source":{"id":"1705.04314","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.04314","created_at":"2026-05-18T00:25:57Z"},{"alias_kind":"arxiv_version","alias_value":"1705.04314v2","created_at":"2026-05-18T00:25:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.04314","created_at":"2026-05-18T00:25:57Z"},{"alias_kind":"pith_short_12","alias_value":"6652XAOYPVWG","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6652XAOYPVWGHVZX","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6652XAOY","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:e9584da65a336b20add422e2afc7ec37f4a1ee6cb33dfd1eed4e74b541b80229","target":"graph","created_at":"2026-05-18T00:25:57Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study the compressible and incompressible two-phase flows separated by a sharp interface with a phase transition and a surface tension. In particular, we consider the problem in $\\mathbb{R}^N$, and the Navier-Stokes-Korteweg equations is used in the upper domain and the Navier-Stokes equations is used in the lower domain. We prove the existence of $\\mathcal{R}$-bounded solution operator families for a resolvent problem arising from its model problem. According to Shibata \\cite{GS2014}, the regularity of $\\rho_+$ is $W^1_q$ in space, but to solve the kinetic equation: $\\mathbf{u}_\\Gamma\\cdot","authors_text":"Keiichi Watanabe","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-10T01:13:39Z","title":"Compressible-incompressible two-phase flows with phase transition: model problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.04314","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8300b737eb1622e537eeabec91fa62743f40fe2b27b8a5c3996b0eb781b7307c","target":"record","created_at":"2026-05-18T00:25:57Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"39bcefe06aef5cc9fc246fa56a0b48a06da83498bee91b3fffe7332a00730dd8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-10T01:13:39Z","title_canon_sha256":"32ae026749436bce79b9d49d38aa2af74603ff38a7550301e97c1451906fe077"},"schema_version":"1.0","source":{"id":"1705.04314","kind":"arxiv","version":2}},"canonical_sha256":"f7bbab81d87d6c63d737c30e957fd57d28732b81d41ce367e8bd009ed3a3cc2a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f7bbab81d87d6c63d737c30e957fd57d28732b81d41ce367e8bd009ed3a3cc2a","first_computed_at":"2026-05-18T00:25:57.862923Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:57.862923Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8N5kIMxoDg47jUUO+YG7ia08TGSFv0GMnK8o6b9RexNMucreJvuUq9UrPQfQO7Gt+Ch5dFPijPCltoXlUxQQBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:57.863651Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.04314","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8300b737eb1622e537eeabec91fa62743f40fe2b27b8a5c3996b0eb781b7307c","sha256:e9584da65a336b20add422e2afc7ec37f4a1ee6cb33dfd1eed4e74b541b80229"],"state_sha256":"ce06d5d886716edb5b233c49ccbd2a5d75be4c64cff3b7b7f285db1942d3351f"}