{"paper":{"title":"Finite-time Singularity Formation for Strong Solutions to the $3D$ Euler Equations, I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"In-Jee Jeong, Tarek M. Elgindi","submitted_at":"2017-08-30T17:23:23Z","abstract_excerpt":"In this paper and the companion paper [EJE2], we establish finite-time singularity formation for finite-energy strong solutions to the axi-symmetric $3D$ Euler equations in the domain $\\{(x,y,z)\\in\\mathbb{R}^3:z^2\\leq c(x^2+y^2)\\}$ for some $c>0$. In the spirit of our previous works, [EJSI] and [EJB], we do this by first studying scale-invariant solutions which satisfy a one dimensional PDE system and proving that they may become singular in finite time for properly chosen initial data. We then prove local well-posedness for the $3D$ Euler equations in a natural regularity class which includes"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.09372","kind":"arxiv","version":2},"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"}