{"paper":{"title":"The motion of whips and chains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Stephen C. Preston","submitted_at":"2011-05-10T13:46:10Z","abstract_excerpt":"We study the motion of an inextensible string (a whip) fixed at one point in the absence of gravity, satisfying the equations $$ \\eta_{tt} = \\partial_s(\\sigma \\eta_s), \\qquad \\sigma_{ss}-\\lvert \\eta_{ss}\\rvert^2 = -\\lvert \\eta_{st}\\rvert^2, \\qquad \\lvert \\eta_s\\rvert^2 \\equiv 1 $$ with boundary conditions $\\eta(t,1)=0$ and $\\sigma(t,0)=0$. We prove local existence and uniqueness in the space defined by the weighted Sobolev energy $$ \\sum_{\\ell=0}^m \\int_0^1 s^{\\ell} \\lvert \\partial_s^{\\ell}\\eta_t\\rvert^2 \\, ds + \\int_0^1 s^{\\ell+1} \\lvert \\partial_s^{\\ell+1}\\eta\\rvert^2 \\, ds, $$ when $m\\ge 3$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.1944","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"}