{"paper":{"title":"Well-posedness of the free-boundary compressible 3-D Euler equations with surface tension and the zero surface tension limit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Daniel Coutand, Jason Hole, Steve Shkoller","submitted_at":"2012-08-13T22:56:56Z","abstract_excerpt":"We prove that the 3-D compressible Euler equations with surface tension along the moving free-boundary are well-posed. Specifically, we consider isentropic dynamics and consider an equation of state, modeling a liquid, given by Courant and Friedrichs as $p(\\rho) = \\alpha \\rho^ \\gamma - \\beta$ for consants $\\gamma >1$ and $ \\alpha, \\beta > 0$. The analysis is made difficult by two competing nonlinearities associated with the potential energy: compression in the bulk, and surface area dynamics on the free-boundary. Unlike the analysis of the incompressible Euler equations, wherein boundary regul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.2726","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"}