{"paper":{"title":"The lifetime of shape oscillations of a bubble in an unbounded, inviscid and compressible fluid with surface tension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","physics.flu-dyn"],"primary_cat":"math.AP","authors_text":"Michael I. Weinstein, Ovidiu Costin, Saleh Tanveer","submitted_at":"2012-10-01T17:58:38Z","abstract_excerpt":"General perturbations of a spherical gas bubble in a compressible and inviscid fluid with surface tension were proved in Shapiro and Weinstein (2011), in the linearized approximation, to decay exponentially, $\\sim e^{-\\Gamma t}, \\Gamma>0$, as time advances. Formal asymptotic and numerical evidence led to the conjecture that $\\Gamma \\approx \\frac{A}{\\epsilon} \\frac{We}{\\epsilon^{2}} \\exp(-B \\frac{We}{\\epsilon^2})$, where $0<\\epsilon\\ll1$ is the Mach number, We is the Weber number, and $A$ and $B$ are positive constants.\n  In this paper, we prove this conjecture and calculate $A$ and $B$ to lead"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.0487","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"}