{"paper":{"title":"A rigidity result for the 3D capillary liquid drop with constant vorticity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Domenico Angelo La Manna, Giuseppe La Scala, Pietro Baldi","submitted_at":"2026-07-01T05:08:38Z","abstract_excerpt":"We consider the free boundary problem for the Euler equations of fluid dynamics governing the motion of a 3D liquid drop with capillarity $\\sigma_0$ and nearly spherical shape, under the assumption of constant vorticity $(0, 0, \\alpha_0)$. First we study the compatibility of the constant vorticity condition with the evolution in time of the system, showing that, for $\\alpha_0 \\neq 0$, any smooth solution with convex domain must satisfy a strong geometrical constraint on the shape of the fluid domain, and that the constant vorticity condition (unlike in the irrotational case $\\alpha_0 = 0$) doe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.00450","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/2607.00450/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"}