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# The lifetime of shape oscillations of a bubble in an unbounded, inviscid and compressible fluid with surface tension

(1 Oct 2012)  Key: citeulike:11357638

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### Abstract

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, $∼ e^-Γ t, Γ>0$, as time advances. Formal asymptotic and numerical evidence led to the conjecture that $Γ ≈ \fracAε \fracWeε^2 \exp(-B \fracWeε^2)$, where $0<ε\ll1$ is the Mach number, We is the Weber number, and $A$ and $B$ are positive constants. In this paper, we prove this conjecture and calculate $A$ and $B$ to leading order in $ε$.