{"paper":{"title":"Enhanced Dissipation, Taylor Dispersion, and Inviscid Damping of Couette flow in the Boussinesq system on the Plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ryan Arbon","submitted_at":"2025-01-01T00:57:34Z","abstract_excerpt":"We consider the quantitative asymptotic stability of the stably stratified Couette flow solution to the 2D fully dissipative nonlinear Boussinesq system on $\\mathbb{R}^2$ with large Richardson number $R > 1/4$, viscosity $\\nu$ and density dissipation $\\kappa$. For an initial perturbation $(\\omega_{in}, \\theta_{in})$ of size $\\mu^{1/2 + \\epsilon}$ in a low-order anisotropic Sobolev space, for $\\mu$ roughly $\\min(\\nu, \\kappa)\\left(1 - O(1/\\sqrt{R})\\right)$ and $\\nu$, $\\kappa$ comparable, we demonstrate asymptotic stability with explicit enhanced dissipation and Taylor dispersion rates of decay. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.00690","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.00690/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"}