{"paper":{"title":"An optimal control problem for the Navier-Stokes-$\\alpha$ system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"\\'Elder J. Villamizar-Roa, Elva Ortega-Torres, Exequiel Mallea-Zepeda","submitted_at":"2019-05-04T03:09:57Z","abstract_excerpt":"In this paper we study a distributed optimal control problem for a three-dimensional Navier-Stokes-$\\alpha$ model. We prove the solvability of the optimal control problem, and derive first-order optimality conditions by using a Lagrange multipliers Theorem. Finally, considering a velocity tracking control problem for the three-dimensional Navier-Stokes-$\\alpha$ model, we analyze the relation of its optimality system to the corresponding one associated to the Navier-Stokes model by proving a convergence theorem, which establishes that, as the length scale $\\alpha$ goes to zero, the optimality s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.01415","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":""},"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"}