{"paper":{"title":"2D hydrodynamical systems: invariant measures of Gaussian type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.flu-dyn"],"primary_cat":"math.PR","authors_text":"Benedetta Ferrario, Hakima Bessaih","submitted_at":"2011-10-09T21:20:31Z","abstract_excerpt":"Gaussian measures $\\mu^{\\beta,\\nu}$ are associated to some stochastic 2D hydrodynamical systems. They are of Gibbsian type and are constructed by means of some invariant quantities of the system depending on some parameter $\\beta$ (related to the 2D nature of the fluid) and the viscosity $\\nu$. We prove the existence and the uniqueness of the global flow for the stochastic viscous system; moreover the measure $\\mu^{\\beta,\\nu}$ is invariant for this flow and is unique. Finally, we prove that the deterministic inviscid equation has a $\\mu^{\\beta,\\nu}$-stationary solution (for any $\\nu>0$)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1887","kind":"arxiv","version":2},"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"}