{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:6NCC7HB32NPK2GYP2OW3WU4T6R","short_pith_number":"pith:6NCC7HB3","schema_version":"1.0","canonical_sha256":"f3442f9c3bd35ead1b0fd3adbb5393f4525348b9f79c0752b7b33c794a725355","source":{"kind":"arxiv","id":"2605.13478","version":1},"attestation_state":"computed","paper":{"title":"Global Yudovich-type solutions to a reduced model for micropolar fluids with zero viscosity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The 2D reduced micropolar fluid model admits global unique Yudovich solutions with only bounded vorticity.","cross_cats":[],"primary_cat":"math.AP","authors_text":"Francesco Fanelli, Pedro Gabriel Fern\\'andez Dalgo","submitted_at":"2026-05-13T13:03:28Z","abstract_excerpt":"In this paper, we study the well-posedeness at low regularity of a two-dimensional system obtained as a reduced model for micropolar fluid dynamics. At the mathematical level, the system presents a coupling between an Euler-type equation for the two-dimensional velocity field of the fluid and an advection-diffusion equation for the scalar microrotation field.\n  For this model, we prove global existence and uniqueness of Yudovich-type solutions, namely weak solutions for which the vorticity is only bounded (with some additional integrability property) and the microrotation field remains bounded"},"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":true,"formal_links_present":false},"canonical_record":{"source":{"id":"2605.13478","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-05-13T13:03:28Z","cross_cats_sorted":[],"title_canon_sha256":"00083f9d8c6ef19c8c0e5bd93f4b337ed4d36130bb7f904b4782f6a60c5c9b6f","abstract_canon_sha256":"48dbd408de4e5808609aa91baabd8ee485f808202024455084e7c635270bc9e1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:41.412768Z","signature_b64":"X+HYOVufis+Bcs1DBJpFgNTrnCzFedoSdHDwQ9OlHH6cjX5ejeV7IBYZhtdewOqR7aFn8JgBe1lShXTnl15qAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f3442f9c3bd35ead1b0fd3adbb5393f4525348b9f79c0752b7b33c794a725355","last_reissued_at":"2026-05-18T02:44:41.412130Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:41.412130Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Global Yudovich-type solutions to a reduced model for micropolar fluids with zero viscosity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The 2D reduced micropolar fluid model admits global unique Yudovich solutions with only bounded vorticity.","cross_cats":[],"primary_cat":"math.AP","authors_text":"Francesco Fanelli, Pedro Gabriel Fern\\'andez Dalgo","submitted_at":"2026-05-13T13:03:28Z","abstract_excerpt":"In this paper, we study the well-posedeness at low regularity of a two-dimensional system obtained as a reduced model for micropolar fluid dynamics. At the mathematical level, the system presents a coupling between an Euler-type equation for the two-dimensional velocity field of the fluid and an advection-diffusion equation for the scalar microrotation field.\n  For this model, we prove global existence and uniqueness of Yudovich-type solutions, namely weak solutions for which the vorticity is only bounded (with some additional integrability property) and the microrotation field remains bounded"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"For this model, we prove global existence and uniqueness of Yudovich-type solutions, namely weak solutions for which the vorticity is only bounded (with some additional integrability property) and the microrotation field remains bounded and of finite energy.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The reduced 2D system obtained from micropolar fluid dynamics with zero viscosity preserves the transport and boundedness properties needed for the Yudovich estimates to close under the given coupling.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Global existence and uniqueness of bounded-vorticity weak solutions is established for a 2D micropolar fluid model with zero viscosity.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The 2D reduced micropolar fluid model admits global unique Yudovich solutions with only bounded vorticity.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"04319332164071cfc20b269e6c0656ca854a42edad76c900b00919560d34f7c5"},"source":{"id":"2605.13478","kind":"arxiv","version":1},"verdict":{"id":"9a43702f-f7a9-46ad-92e2-fad4f374953c","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T19:30:31.161902Z","strongest_claim":"For this model, we prove global existence and uniqueness of Yudovich-type solutions, namely weak solutions for which the vorticity is only bounded (with some additional integrability property) and the microrotation field remains bounded and of finite energy.","one_line_summary":"Global existence and uniqueness of bounded-vorticity weak solutions is established for a 2D micropolar fluid model with zero viscosity.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The reduced 2D system obtained from micropolar fluid dynamics with zero viscosity preserves the transport and boundedness properties needed for the Yudovich estimates to close under the given coupling.","pith_extraction_headline":"The 2D reduced micropolar fluid model admits global unique Yudovich solutions with only bounded vorticity."},"references":{"count":26,"sample":[{"doi":"","year":2024,"title":"Instability and non-uniqueness for the 2D Euler equations, after M. Vishik","work_id":"fed3a777-b20d-48f3-8120-fc9edd955bef","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2011,"title":"Fourier analysis and nonlinear partial differential equa- tions","work_id":"d1788d0e-c9d8-4ab8-8a2a-ec6bc127a0d6","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2022,"title":"A. Béjar-López, C. Cunha, J. Soler:Two-dimensional incompressible micropolar fluid models with singular initial data. Phys. D.,430(2022), Paper No. 133069","work_id":"8b6c6a58-3a81-4796-899d-d3b0c8774b4f","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1991,"title":"Chemin:Sur le mouvement des particules d’un fluide parfait incompressible bidimensionel","work_id":"f9371721-029a-48b5-a667-de77a390d3e5","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1993,"title":"Chemin:Persistance des structures géométriques liées aux poches de tourbillon","work_id":"8fd5071d-fb62-4393-82a3-c620e131c974","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":26,"snapshot_sha256":"c9a1bf0af947e91f2edc0647961a69bdc450f4fceabe386897f576ea8b3a7fde","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":"2605.13478","created_at":"2026-05-18T02:44:41.412213+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.13478v1","created_at":"2026-05-18T02:44:41.412213+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.13478","created_at":"2026-05-18T02:44:41.412213+00:00"},{"alias_kind":"pith_short_12","alias_value":"6NCC7HB32NPK","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_16","alias_value":"6NCC7HB32NPK2GYP","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_8","alias_value":"6NCC7HB3","created_at":"2026-05-18T12:33:37.589309+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/6NCC7HB32NPK2GYP2OW3WU4T6R","json":"https://pith.science/pith/6NCC7HB32NPK2GYP2OW3WU4T6R.json","graph_json":"https://pith.science/api/pith-number/6NCC7HB32NPK2GYP2OW3WU4T6R/graph.json","events_json":"https://pith.science/api/pith-number/6NCC7HB32NPK2GYP2OW3WU4T6R/events.json","paper":"https://pith.science/paper/6NCC7HB3"},"agent_actions":{"view_html":"https://pith.science/pith/6NCC7HB32NPK2GYP2OW3WU4T6R","download_json":"https://pith.science/pith/6NCC7HB32NPK2GYP2OW3WU4T6R.json","view_paper":"https://pith.science/paper/6NCC7HB3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.13478&json=true","fetch_graph":"https://pith.science/api/pith-number/6NCC7HB32NPK2GYP2OW3WU4T6R/graph.json","fetch_events":"https://pith.science/api/pith-number/6NCC7HB32NPK2GYP2OW3WU4T6R/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6NCC7HB32NPK2GYP2OW3WU4T6R/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6NCC7HB32NPK2GYP2OW3WU4T6R/action/storage_attestation","attest_author":"https://pith.science/pith/6NCC7HB32NPK2GYP2OW3WU4T6R/action/author_attestation","sign_citation":"https://pith.science/pith/6NCC7HB32NPK2GYP2OW3WU4T6R/action/citation_signature","submit_replication":"https://pith.science/pith/6NCC7HB32NPK2GYP2OW3WU4T6R/action/replication_record"}},"created_at":"2026-05-18T02:44:41.412213+00:00","updated_at":"2026-05-18T02:44:41.412213+00:00"}