{"paper":{"title":"Selection of quasi-stationary states in the Navier-Stokes equation on the torus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Eric Cooper, Konstantinos Spiliopoulos, Margaret Beck","submitted_at":"2017-01-17T20:00:05Z","abstract_excerpt":"The two dimensional incompressible Navier-Stokes equation on $D_\\delta := [0, 2\\pi\\delta] \\times [0, 2\\pi]$ with $\\delta \\approx 1$, periodic boundary conditions, and viscosity $0 < \\nu \\ll 1$ is considered. Bars and dipoles, two explicitly given quasi-stationary states of the system, evolve on the time scale $\\mathcal{O}(e^{-\\nu t})$ and have been shown to play a key role in its long-time evolution. Of particular interest is the role that $\\delta$ plays in selecting which of these two states is observed. Recent numerical studies suggest that, after a transient period of rapid decay of the hig"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.04850","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"}