{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:444IHCXYWFG5U6YUJAKEMWI7U7","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":"3297b2691363753448b1670ebd8c191dfa12f2a5f6c07b13ccc7d6234f512219","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2025-05-09T20:43:25Z","title_canon_sha256":"be7f7df0fd0a1411d05f4afc51d93a76b4bd43eba305813359c93b65e0831d8c"},"schema_version":"1.0","source":{"id":"2505.06423","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.06423","created_at":"2026-07-05T11:01:09Z"},{"alias_kind":"arxiv_version","alias_value":"2505.06423v1","created_at":"2026-07-05T11:01:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.06423","created_at":"2026-07-05T11:01:09Z"},{"alias_kind":"pith_short_12","alias_value":"444IHCXYWFG5","created_at":"2026-07-05T11:01:09Z"},{"alias_kind":"pith_short_16","alias_value":"444IHCXYWFG5U6YU","created_at":"2026-07-05T11:01:09Z"},{"alias_kind":"pith_short_8","alias_value":"444IHCXY","created_at":"2026-07-05T11:01:09Z"}],"graph_snapshots":[{"event_id":"sha256:72bf948865cefe281326a6c6eabacb499e0a267b68fcba241449c03942716fe6","target":"graph","created_at":"2026-07-05T11:01:09Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2505.06423/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we consider the flow of two incompressible, viscous and immiscible fluids in a bounded domain, with different densities and viscosities. This model consists of a coupled system of Navier-Stokes and Mullins-Sekerka type parts, and can be obtained from the sharp interface limit of the diffuse interface model proposed by the first author, Garcke, and Gr\\\"{u}n (Math. Models Methods Appl. Sci. 22, 2012). We introduce a new notion of weak solutions and prove its global in time existence, together with a consistency result of smooth weak solutions with the classical Navier-Stokes-Mullin","authors_text":"Andrea Poiatti, Helmut Abels","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2025-05-09T20:43:25Z","title":"Weak Solutions to a Sharp Interface Model for a Two-Phase Flow of Incompressible Viscous Fluids with Different Densities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.06423","kind":"arxiv","version":1},"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":"sha256:35166abec760c139c4a4016651cffc160096c6ac4824cc118b083367a2c64e02","target":"record","created_at":"2026-07-05T11:01:09Z","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":"3297b2691363753448b1670ebd8c191dfa12f2a5f6c07b13ccc7d6234f512219","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2025-05-09T20:43:25Z","title_canon_sha256":"be7f7df0fd0a1411d05f4afc51d93a76b4bd43eba305813359c93b65e0831d8c"},"schema_version":"1.0","source":{"id":"2505.06423","kind":"arxiv","version":1}},"canonical_sha256":"e738838af8b14dda7b14481446591fa7ee552b8621dfa00bd797e667a765b8fd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e738838af8b14dda7b14481446591fa7ee552b8621dfa00bd797e667a765b8fd","first_computed_at":"2026-07-05T11:01:09.305441Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:01:09.305441Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vERd9+bEPfNxc79XkXgyDCwWkll4X5UkJzFsXeHLI4E4jBmKX18PJ8l9Pk031bcMlVI6uItjPBcE2n34o+DsAw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:01:09.305929Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.06423","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:35166abec760c139c4a4016651cffc160096c6ac4824cc118b083367a2c64e02","sha256:72bf948865cefe281326a6c6eabacb499e0a267b68fcba241449c03942716fe6"],"state_sha256":"c1cc4a34d3bb109c80239f7312538f8779888860205ef28e0f13d0ea62de9c56"}