{"paper":{"title":"On the relation between enhanced dissipation time-scales and mixing rates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.AP","authors_text":"Matias G. Delgadino, Michele Coti Zelati, Tarek M. Elgindi","submitted_at":"2018-06-08T16:02:21Z","abstract_excerpt":"We study diffusion and mixing in different linear fluid dynamics models, mainly related to incompressible flows. In this setting, mixing is a purely advective effect which causes a transfer of energy to high frequencies. When diffusion is present, mixing enhances the dissipative forces. This phenomenon is referred to as enhanced dissipation, namely the identification of a time-scale faster than the purely diffusive one. We establish a precise connection between quantitative mixing rates in terms of decay of negative Sobolev norms and enhanced dissipation time-scales. The proofs are based on a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.03258","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":""},"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"}