{"paper":{"title":"Quartic Lyapunov functions for global fluid stability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.flu-dyn","authors_text":"David Darrow, David Goluskin, Elizabeth Carlson","submitted_at":"2026-06-16T17:56:08Z","abstract_excerpt":"A fluid system is 'globally stable' if all initial conditions eventually converge to the same state. Since Reynolds (1895) and Orr (1907), the standard way to show global stability has been the energy method, which uses the fluctuation energy as a Lyapunov function. However, the energy method fails whenever transient energy growth is possible, so it often yields overly strict stability criteria. The first broadly applicable alternative has recently been introduced (Goulart & Chernyshenko 2012; Fuentes et al. 2022), using polynomial optimization to construct non-quadratic Lyapunov functions. Un"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.18232","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/2606.18232/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"}