{"paper":{"title":"On the weak formulation of Prandtl's minimum drag problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Aram L. Karakhanyan, Yigit Katgi","submitted_at":"2026-06-10T23:55:43Z","abstract_excerpt":"We study Prandtl's classical problem on minimising the induced drag for a finite wing with fixed span. The induced drag is given by a singular quadratic functional of the circulation, with admissible functions satisfying the prescribed lift and second-moment conditions. We formulate the problem in the fractional Sobolev space \\(H^{1/2}\\), which is the natural energy space for the functional, prove existence and uniqueness of minimisers by variational methods, and derive the corresponding Euler--Lagrange equation. %\nPassing to a periodic formulation on the one-dimensional torus, we identify the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.12757","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/2606.12757/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"}