{"paper":{"title":"A Verification Theorem for an Optimal Control Problem Governed by the Convective Brinkman--Forchheimer Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Manil T. Mohan, Sagar Gautam","submitted_at":"2026-06-25T17:29:07Z","abstract_excerpt":"This article establishes a verification theorem for an optimal control problem governed by the two- and three-dimensional convective Brinkman--Forchheimer equations on the $d$-dimensional torus, $d\\in\\{2,3\\}$:\n  $$\\frac{\\partial\\mathfrak{u}}{\\partial t}\n  -\\mu\\Delta\\mathfrak{u}\n  +(\\mathfrak{u}\\cdot\\nabla)\\mathfrak{u}\n  +\\alpha\\mathfrak{u}\n  +\\beta|\\mathfrak{u}|^{r-1}\\mathfrak{u}\n  +\\nabla\\mathfrak{p}\n  =\\boldsymbol{f},\n  \\qquad\n  \\nabla\\cdot\\mathfrak{u}=0,$$\n  where $\\mu,\\alpha,\\beta>0$ and $r\\in[1,\\infty)$. We derive the Pontryagin maximum principle and develop a verification framework for t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.27312","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/2606.27312/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"}