{"paper":{"title":"Self-Similar Solutions of the Two-Dimensional Incompressible Euler Equation from Large Initial Data","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hyungjun Choi","submitted_at":"2026-07-22T03:05:04Z","abstract_excerpt":"Let $\\frac{1}{3}<a<1$ and let $u_0$ be a $C^1$, divergence-free, $(-a)$-homogeneous vector field on $\\mathbb{R}^2\\setminus\\{0\\}$. We construct a forward-in-time self-similar solution of the two-dimensional incompressible Euler equations, \\[ u(t,x)=t^{-\\frac{a}{1+a}} U\\left(\\frac{x}{t^{{\\frac{1}{1+a}}}}\\right), \\] with initial datum $u_0$. No smallness or sign assumption is imposed on the initial datum. The construction is a vanishing-dissipation limit of the hypodissipative self-similar profiles. The key is a vorticity profile estimate, uniform in the dissipation parameter, in the critical Lor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.19700","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/2607.19700/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"}