{"paper":{"title":"Formation of shocks for 2D isentropic compressible Euler","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.flu-dyn"],"primary_cat":"math.AP","authors_text":"Steve Shkoller, Tristan Buckmaster, Vlad Vicol","submitted_at":"2019-07-08T18:01:18Z","abstract_excerpt":"We consider the 2D isentropic compressible Euler equations, with pressure law $p(\\rho) = (\\sfrac{1}{\\gamma}) \\rho^\\gamma$, with $\\gamma >1$. We provide an elementary constructive proof of shock formation from smooth initial datum of finite energy, with no vacuum regions, and with {nontrivial vorticity}. We prove that for initial data which has minimum slope $- {\\sfrac{1}{ \\eps}}$, for $ \\eps>0$ taken sufficiently small relative to the $\\OO(1)$ amplitude, there exist smooth solutions to the Euler equations which form a shock in time $\\OO(\\eps)$. The blowup time and location can be explicitly co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.03784","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"}