{"paper":{"title":"Exponential self-similar mixing by incompressible flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Anna L. Mazzucato, Gianluca Crippa, Giovanni Alberti","submitted_at":"2016-05-06T20:21:38Z","abstract_excerpt":"We study the problem of the optimal mixing of a passive scalar under the action of an incompressible flow in two space dimensions. The scalar solves the continuity equation with a divergence-free velocity field, which satisfies a bound in the Sobolev space $W^{s,p}$, where $s \\geq 0$ and $1\\leq p\\leq \\infty$. The mixing properties are given in terms of a characteristic length scale, called the mixing scale. We consider two notions of mixing scale, one functional, expressed in terms of the homogeneous Sobolev norm $\\dot H^{-1}$, the other geometric, related to rearrangements of sets. We study r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.02090","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"}