{"paper":{"title":"Invariant measures for passive scalars in the small noise inviscid limit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.AP","authors_text":"Jacob Bedrossian, Michele Coti Zelati, Nathan Glatt-Holtz","submitted_at":"2015-05-27T14:47:56Z","abstract_excerpt":"We consider a class of invariant measures for a passive scalar $f$ driven by an incompressible velocity field $\\boldsymbol{u}$, on a $d$-dimensional periodic domain, satisfying $$ \\partial_t f + \\boldsymbol{u} \\cdot \\nabla f = 0, \\qquad f(0)=f_0. $$ The measures are obtained as limits of stochastic viscous perturbations. We prove that the span of the $H^1$ eigenfunctions of the operator $\\boldsymbol{u}\\cdot\\nabla$ contains the support of these measures. We also analyze several explicit examples: when $\\boldsymbol{u}$ is a shear flow or a relaxation enhancing flow (a generalization of weakly mi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.07356","kind":"arxiv","version":3},"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"}