{"paper":{"title":"Stability Results for Idealised Shear Flows on a Rectangular Periodic Domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Holger Dullin, Joachim Worthington","submitted_at":"2016-08-22T10:26:33Z","abstract_excerpt":"We present a new linearly stable solution of the Euler fluid flow on a torus. On a two-dimensional rectangular periodic domain $[0,2\\pi)\\times[0,2\\pi / \\kappa)$ for $\\kappa\\in\\mathbb{R}^+$, the Euler equations admit a family of stationary solutions given by the vorticity profiles $\\Omega^*(\\mathbf{x})= \\Gamma \\cos(p_1x_1+ \\kappa p_2x_2)$. We show linear stability for such flows when $p_2=0$ and $\\kappa \\geq |p_1|$ (equivalently $p_1=0$ and $\\kappa{|p_2|}\\leq{1}$). The classical result due to Arnold is that for $p_1 = 1, p_2 = 0$ and $\\kappa \\ge 1$ the stationary flow is {nonlinearly} stable vi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.06109","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"}