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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 $m\\ge 3$"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1105.1944","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-05-10T13:46:10Z","cross_cats_sorted":[],"title_canon_sha256":"5877f3944a3cb30b5a9ead95d9f97e9c368fa7c2035879e06ac07735f468d48d","abstract_canon_sha256":"fc718aecedb5f80ae5d1b5351c1af2012ed3c155abbae5f0a126718bbeba5796"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:22:30.242251Z","signature_b64":"rDB2H6bBJAkQQmawL/JZaU6RtFhjXz/spXQTpg4jiWBsTuIADzl7zEFX1nCFvNXsKDrc8wNbGA2/2YLt73aMAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ba9344d7425ab538e40bead13810d5691eb72567fbbdf934fb57f44090c7be0","last_reissued_at":"2026-05-18T04:22:30.241762Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:22:30.241762Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1105.1944","created_at":"2026-05-18T04:22:30.241823+00:00"},{"alias_kind":"arxiv_version","alias_value":"1105.1944v1","created_at":"2026-05-18T04:22:30.241823+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.1944","created_at":"2026-05-18T04:22:30.241823+00:00"},{"alias_kind":"pith_short_12","alias_value":"POUTITLUEWVV","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_16","alias_value":"POUTITLUEWVVHDSA","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_8","alias_value":"POUTITLU","created_at":"2026-05-18T12:26:39.201973+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/POUTITLUEWVVHDSAX2WRHAINK2","json":"https://pith.science/pith/POUTITLUEWVVHDSAX2WRHAINK2.json","graph_json":"https://pith.science/api/pith-number/POUTITLUEWVVHDSAX2WRHAINK2/graph.json","events_json":"https://pith.science/api/pith-number/POUTITLUEWVVHDSAX2WRHAINK2/events.json","paper":"https://pith.science/paper/POUTITLU"},"agent_actions":{"view_html":"https://pith.science/pith/POUTITLUEWVVHDSAX2WRHAINK2","download_json":"https://pith.science/pith/POUTITLUEWVVHDSAX2WRHAINK2.json","view_paper":"https://pith.science/paper/POUTITLU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1105.1944&json=true","fetch_graph":"https://pith.science/api/pith-number/POUTITLUEWVVHDSAX2WRHAINK2/graph.json","fetch_events":"https://pith.science/api/pith-number/POUTITLUEWVVHDSAX2WRHAINK2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/POUTITLUEWVVHDSAX2WRHAINK2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/POUTITLUEWVVHDSAX2WRHAINK2/action/storage_attestation","attest_author":"https://pith.science/pith/POUTITLUEWVVHDSAX2WRHAINK2/action/author_attestation","sign_citation":"https://pith.science/pith/POUTITLUEWVVHDSAX2WRHAINK2/action/citation_signature","submit_replication":"https://pith.science/pith/POUTITLUEWVVHDSAX2WRHAINK2/action/replication_record"}},"created_at":"2026-05-18T04:22:30.241823+00:00","updated_at":"2026-05-18T04:22:30.241823+00:00"}