Minnaert resonances for acoustic waves in bubbly media
  Through the application of layer potential techniques and Gohberg-Sigal theory we derive an original formula for the Minnaert resonance frequencies of arbitrarily shaped bubbles. We also provide a mathematical justification for the monopole approximation of scattering of acoustic waves by bubbles at their Minnaert resonant frequency. Our results are complemented by several numerical examples which serve to validate our formula in two dimensions. 
Habib Ammari, Brian Fitzpatrick, David Gontier, Hyundae Lee and Hai   Zhang
math.AP