{"paper":{"title":"Conditional regularity for the compressible Navier-Stokes equations with potential temperature transport","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andreas Sch\\\"omer, M\\'aria Luk\\'a\\v{c}ov\\'a-Medvi\\v{d}ov\\'a","submitted_at":"2024-07-20T11:34:53Z","abstract_excerpt":"We study conditional regularity for the compressible Navier-Stokes equations with potential temperature transport in a bounded domain $\\Omega\\subset\\mathbb{R}^d$, $d\\in\\{2,3\\}$, with no-slip boundary conditions. We first prove the existence and uniqueness of local-in-time strong solutions. Further, we prove a blow-up criterion for the strong solution in terms of $L^\\infty$-norms for the density and the velocity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.14849","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/2407.14849/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"}