{"paper":{"title":"Prandtl-Batchelor flows with a point vortex on a disk","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jianfeng Zhao, Mingwen Fei, Zhi Chen, Zhiwu Lin","submitted_at":"2024-10-10T09:38:19Z","abstract_excerpt":"In this paper we aim to construct a very weak solution to the steady two-dimensional Navier-Stokes equations which is affected by an external force induced by a point vortex on the unit disk. Such a solution is also the form of Prandtl-Batchelor type, i.e. the vorticity in the limit of vanishing viscosity is constant in an inner region separated from the boundary layer. Multi-scale asymptotic analysis which will capture well the singular behavior of the solution is used to construct higher order approximate solutions of the Navier-Stokes equations firstly, and then stability analysis is perfor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.07759","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.07759/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","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"}