{"paper":{"title":"Interior Structural Bifurcation of 2D Symmetric Incompressible Flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","physics.flu-dyn"],"primary_cat":"math-ph","authors_text":"Ali Deliceo\\u{g}lu, Deniz Bozkurt, Taylan \\c{S}eng\\\"ul","submitted_at":"2017-12-05T17:46:02Z","abstract_excerpt":"The structural bifurcation of a 2D divergence free vector field $\\mathbf{u}(\\cdot, t)$ when $\\mathbf{u}(\\cdot, t_0)$ has an interior isolated singular point $\\mathbf{x}_0$ of zero index has been studied by Ma and Wang. Although in the class of divergence free fields which undergo a local bifurcation around a singular point, the ones with index zero singular points are generic, this class excludes some important families of symmetric flows. In particular, when $\\mathbf{u}(\\cdot, t_0)$ is anti-symmetric with respect to $\\mathbf{x}_0$, or symmetric with respect to the axis located on $\\mathbf{x}_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.01784","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"}