{"paper":{"title":"2D homogeneous solutions to the Euler equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Roman Shvydkoy, Xue Luo","submitted_at":"2014-09-15T16:49:37Z","abstract_excerpt":"In this paper we study classification of homogeneous solutions to the stationary Euler equation with locally finite energy. Written in the form $u = \\nabla^\\perp \\Psi$, $\\Psi(r,\\theta) = r^{\\lambda} \\psi(\\theta)$, for $\\lambda >0$, we show that only trivial solutions exist in the range $0<\\lambda<1/2$, i.e. parallel shear and rotational flows. In other cases many new solutions are exhibited that have hyperbolic, parabolic and elliptic structure of streamlines. In particular, for $\\lambda>9/2$ the number of different non-trivial elliptic solutions is equal to the cardinality of the set $(2,\\sqr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.4322","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"}