{"paper":{"title":"Enhanced dissipation and stability of Poiseuille flow for two-dimensional Boussinesq system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gaofeng Wang","submitted_at":"2024-05-20T05:09:36Z","abstract_excerpt":"We investigate the nonlinear stability problem for the two-dimensional Boussinesq system around the Poiseuille flow in a finite channel. The system has the characteristic of Navier-slip boundary condition for the velocity and Dirichlet boundary condition for the temperature, with a small viscosity $\\nu$ and small thermal diffusion $\\mu,$ respectively. More precisely, we prove that if the initial velocity and initial temperature satisfies$$||u_{0}-(1-y^2,0) ||_{H^{\\frac{7}{2}+}}\\leq c_0\\min\\left\\lbrace \\mu,\\nu\\right\\rbrace ^{\\frac{2}{3}}$$ and $$ ||\\theta_{0}||_{H^1}+|||D_x|^{\\frac{1}{8}}\\theta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.11787","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2405.11787/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"}