{"paper":{"title":"Long time dynamics for helical vortex filament in Euler flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dengjun Guo, Lifeng Zhao","submitted_at":"2024-03-14T03:28:17Z","abstract_excerpt":"We consider the three-dimensional incompressible Euler equation \\begin{equation*}\\left\\{\\begin{aligned} &\\partial_t \\Omega+U \\cdot \\nabla \\Omega-\\Omega\\cdot \\nabla U=0 \\\\ &\\Omega(x,0)=\\Omega_0(x) \\end{aligned}\\right. \\end{equation*} under the assumption that $\\Omega^z$ is helical and in the absence of vorticity stretching. Assuming that the initial vorticity $\\Omega_0$ is primarily concentrated within an $\\epsilon$ neighborhood of a helix $\\Gamma_0$, we prove that its solution $\\Omega(\\cdot,t)$ remain concentrated near a helix $\\Gamma(t)$ for any $t \\in [0,T)$, where $\\Gamma(t)$ can be interpr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.09071","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/2403.09071/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"}