{"paper":{"title":"Local existence of strong solutions to the $k-\\varepsilon$ model equations for turbulent flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Baoquan Yuan, Guoquan Qin","submitted_at":"2015-07-11T09:46:19Z","abstract_excerpt":"In this paper, we are concerned with the local existence of strong solutions to the $k-\\varepsilon$ model equations for turbulent flows in a bounded domain $\\Omega$$\\subset$ $\\mathbb{R}^{3}$. We prove the existence of unique local strong solutions under the assumption that turbulent kinetic energy and the initial density both have lower bounds away from zero."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.03083","kind":"arxiv","version":2},"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"}