{"paper":{"title":"Dimension Reduction of Compressible Fluid Models over Product Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.flu-dyn"],"primary_cat":"math.AP","authors_text":"Siran Li","submitted_at":"2017-10-15T05:25:13Z","abstract_excerpt":"In this paper we study the dimension reduction limits of the compressible Navier--Stokes equations over product Riemannian manifolds $\\mathcal{O}_\\epsilon \\cong \\mathcal{M} \\times \\epsilon\\mathcal{F}$, such that $\\dim\\,(\\mathcal{M})=n$ and $\\dim\\,(\\mathcal{F})=d$ are arbitrary. Using the method of relative entropies, we establish the convergence of the suitable weak solutions of the Navier--Stokes equations on $\\mathcal{O}_\\epsilon$ to the classical solution of the limiting equations on $\\mathcal{M}$ as $\\epsilon \\rightarrow 0^+$, provided the latter exists. In addition, we also deduce the van"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.05275","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"}