{"paper":{"title":"Rigorous justification of the hydrostatic-incompressible approximation for weakly stratified isothermal flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Quyuan Lin, Xin Liu","submitted_at":"2026-07-29T21:37:24Z","abstract_excerpt":"We consider the limit of small Mach number and small vertical-to-horizontal aspect ratio for the isothermal compressible Navier-Stokes system. In addition, we consider the scale in which the stratification is weak. Owing to the anisotropic nature of the problem, the dynamics exhibit a three-wave separation phenomenon, consistent of a slow wave, a fast horizontal acoustic wave, and an even faster vertical acoustic wave. These three waves, unfortunately, are not mutually orthogonal, and the corresponding projections are parametrized by the small parameter, which significantly complicates the non"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.27477","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/2607.27477/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"}