{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:GW56UUYRAFOS4OZTIMIAQGCA7T","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":"b4194c55edee81a217baf36d7c3e03e92e8d3e98d54f4a9ab5a2f75e0f80f8be","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-06-29T09:25:17Z","title_canon_sha256":"a9bb0ca332f33bdc14043bed6bccb3d9eb2385c7fad7695fb4ff54a7e9a8c181"},"schema_version":"1.0","source":{"id":"2606.30022","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.30022","created_at":"2026-06-30T02:17:46Z"},{"alias_kind":"arxiv_version","alias_value":"2606.30022v1","created_at":"2026-06-30T02:17:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.30022","created_at":"2026-06-30T02:17:46Z"},{"alias_kind":"pith_short_12","alias_value":"GW56UUYRAFOS","created_at":"2026-06-30T02:17:46Z"},{"alias_kind":"pith_short_16","alias_value":"GW56UUYRAFOS4OZT","created_at":"2026-06-30T02:17:46Z"},{"alias_kind":"pith_short_8","alias_value":"GW56UUYR","created_at":"2026-06-30T02:17:46Z"}],"graph_snapshots":[{"event_id":"sha256:1e36333bd062d1b4d871dbb9e462e494f76d3047188456d355f68a6d6fb2b99c","target":"graph","created_at":"2026-06-30T02:17:46Z","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/2606.30022/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we study a particular family of solutions of the Vlasov-Navier-Stokes system posed on $\\mathbb{R}^d$ (with $d\\geq 2$), and show their convergence to the unique solution of the pressureless Euler-Navier-Stokes system. A global existence result for the latter system, in the small data regime, was established in \\cite{MonENS}. Here we place ourselves in a multiphase framework, introduced and studied by Zakharov in \\cite{Zakharov1,Zakharov2}, in order to carry out an analogous analysis for a system that we will call multiphase pressureless Euler-Navier-Stokes. We then study the sing","authors_text":"Valentin Lemarie (LAMA)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-06-29T09:25:17Z","title":"Multiphase formulation of the Vlasov-Navier-Stokes equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30022","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:c8d9f6bc4e5f1a00194e4f065c07bb8481dddc89739351fa5e35210670ca3dd7","target":"record","created_at":"2026-06-30T02:17:46Z","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":"b4194c55edee81a217baf36d7c3e03e92e8d3e98d54f4a9ab5a2f75e0f80f8be","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-06-29T09:25:17Z","title_canon_sha256":"a9bb0ca332f33bdc14043bed6bccb3d9eb2385c7fad7695fb4ff54a7e9a8c181"},"schema_version":"1.0","source":{"id":"2606.30022","kind":"arxiv","version":1}},"canonical_sha256":"35bbea5311015d2e3b334310081840fccf57e4fcd3b5a00d167d24d82971da83","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"35bbea5311015d2e3b334310081840fccf57e4fcd3b5a00d167d24d82971da83","first_computed_at":"2026-06-30T02:17:46.401182Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-30T02:17:46.401182Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Vuw1HQQqE6FvqM5Z0Jz3jP2r08hwfFdweBs/N7gkr2fOrI53rqebf2vK2NnTB8Pq2daAwRPYxzSp/1xgVEQkCg==","signature_status":"signed_v1","signed_at":"2026-06-30T02:17:46.401665Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.30022","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c8d9f6bc4e5f1a00194e4f065c07bb8481dddc89739351fa5e35210670ca3dd7","sha256:1e36333bd062d1b4d871dbb9e462e494f76d3047188456d355f68a6d6fb2b99c"],"state_sha256":"967a696e98c834bc81b41275a325703d5e957b92b61a858b8dda581c3bd46b89"}