{"paper":{"title":"On the persistence of H\\\"older regular patches of density for the inhomogeneous Navier-Stokes equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Rapha\\\"el Danchin, Xin Zhang","submitted_at":"2016-12-01T14:53:19Z","abstract_excerpt":"In  our recent work dedicated to   the Boussinesq equations [Danchin and Zhang 2016], we established the persistence of solutions with piecewise constant temperature along interfaces with H\\\"older regularity. We here address the same problem for   the inhomogeneous Navier-Stokes equations satisfied by a viscous incompressibleand inhomogeneous fluid. We establish that, indeed, in the slightly inhomogeneous case, patches of densities with $\\mathcal{C}^{1, \\varepsilon}$ regularity propagate for all time. As in   [Danchin and Zhang 2016],   our result follows from the conservation of H\\\"older regu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.00282","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"}