{"paper":{"title":"Error estimates for an unregularized optimal control problem for the stationary Navier-Stokes equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Error estimates are proven for variational discretization of an unregularized optimal control problem for the stationary Navier-Stokes equations, for nonsingular locally optimal controls satisfying a growth condition that implies bang-bang structure.","cross_cats":["cs.NA","math.OC"],"primary_cat":"math.NA","authors_text":"Francisco Fuica, Nicolai Jork","submitted_at":"2026-05-02T22:48:52Z","abstract_excerpt":"We consider an unregularized optimal control problem subject to the steady-state Navier-Stokes equations. We derive the existence of optimal solutions and prove first- and second-order optimality conditions. To approximate solutions to the optimal control problem, we consider the variational discretization scheme. We analyze convergence properties of the discretization and prove a priori error estimates for locally optimal controls that are nonsingular and which satisfy a growth condition which implies a bang-bang structure. We also propose a residual-type a posteriori error estimator that acc"},"claims":{"count":3,"items":[{"kind":"strongest_claim","text":"We prove a priori error estimates for locally optimal controls that are nonsingular and which satisfy a growth condition which implies a bang-bang structure.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The locally optimal controls are nonsingular and satisfy a growth condition implying bang-bang structure (as stated in the abstract for the error estimates to hold).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Error estimates are proven for variational discretization of an unregularized optimal control problem for the stationary Navier-Stokes equations, for nonsingular locally optimal controls satisfying a growth condition that implies bang-bang structure.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"}],"snapshot_sha256":"5ccddcf876b9418d95f8b13871bb3b3dd2df3da499b6a2f54f1d2c90682ca9f6"},"source":{"id":"2605.01633","kind":"arxiv","version":2},"verdict":{"id":"a35da9a7-e0b5-44af-9fe2-c8e98d601351","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-08T19:35:04.792798Z","strongest_claim":"We prove a priori error estimates for locally optimal controls that are nonsingular and which satisfy a growth condition which implies a bang-bang structure.","one_line_summary":"Error estimates are proven for variational discretization of an unregularized optimal control problem for the stationary Navier-Stokes equations, for nonsingular locally optimal controls satisfying a growth condition that implies bang-bang structure.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The locally optimal controls are nonsingular and satisfy a growth condition implying bang-bang structure (as stated in the abstract for the error estimates to hold).","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.01633/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-20T17:38:58.820124Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T17:06:57.116736Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"2bfb27d38b1dd5ff2da366327d2e3d96453e0096607c5a810333ada2d70acf6e"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"5626af1298d79e5c37bf7a21a0d0cd68d1e36420e205f16e32098a9e8b87fe13"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}