{"paper":{"title":"Existence of stationary measures for partially damped SDEs with generic, Euler-type nonlinearities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Alex Blumenthal, Jacob Bedrossian, Keagan Callis, Kyle Liss","submitted_at":"2024-07-23T15:49:03Z","abstract_excerpt":"We study nonlinear energy transfer and the existence of stationary measures in a class of degenerately forced SDEs on $\\mathbb R^d$ with a quadratic, conservative nonlinearity $B(x,x)$ constrained to possess various properties common to finite-dimensional fluid models and a linear damping term $-Ax$ that acts only on a proper subset of phase space in the sense that $\\mathrm{dim}(\\mathrm{ker}A) \\gg 1$. Existence of a stationary measure is straightforward if $\\mathrm{ker}A = \\{0\\}$, but when the kernel of $A$ is nontrivial a stationary measure can exist only if the nonlinearity transfers enough "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.16592","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/2407.16592/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"}