{"paper":{"title":"Exact Area Law for Planar Loops in Turbulence in Two and Three Dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.CD","physics.flu-dyn"],"primary_cat":"hep-th","authors_text":"Alexander Migdal","submitted_at":"2019-04-10T15:37:03Z","abstract_excerpt":"We study properties of the minimal surface in the Area Law Solution \\cite{M93}, \\cite{M19a}, \\cite{M19b}. We find out that Area Law holds exactly for 2D turbulence as well as for arbitrary planar loop in higher dimensions. This relies on our previous result $\\alpha = \\frac{1}{2}$ in which case the second moment of circulation can be proven to reduce to the area inside the planar loop. In $d=3$, we demonstrate how the Stokes condition $\\partial_i \\omega_i(r)=0$ is exactly satisfied for the minimal surface solution in virtue of vanishing mean curvature at the minimal surface. In order to satisfy"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.05245","kind":"arxiv","version":3},"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"}