{"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"}