{"paper":{"title":"Dynamics and leapfrogging phenomena of multiple helical vortices for 3D incompressible Euler equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Daomin Cao, Guolin Qin, Jie Wan, Junhong Fan","submitted_at":"2025-05-18T05:33:36Z","abstract_excerpt":"In this paper, we investigate the time evolution of helical vortices without swirl for the incompressible Euler equations in $\\mathbb R^3$ under general initial assumptions. Assume the initial helical vorticity is sharply concentrated in $N$ distinct $\\ep$-neighborhoods, whose mutual distances vanish as $O(1/|\\ln \\ep|)$, and each vortex core possesses vorticity mass of order $1/|\\ln \\ep|^{1+b}$ for an arbitrary fixed $b\\in\\mathbb R$. We prove that as $\\ep\\to 0$, the motion of these helical vortices converges uniformly to a dynamical system derived herein over a time interval of order $1/|\\ln\\v"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.12240","kind":"arxiv","version":4},"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/2505.12240/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"}