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

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, $\sim e^{-\Gamma t},\Gamma >0$, 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 $0<\epsilon \ll 1$ 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 $\epsilon$.

14 pages, submitted