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.
Cite this article
Habib Ammari, Brian Fitzpatrick, David Gontier, Hyundae Lee, Hai Zhang, Minnaert resonances for acoustic waves in bubbly media. Ann. Inst. H. Poincaré Anal. Non Linéaire 35 (2018), no. 7, pp. 1975–1998DOI 10.1016/J.ANIHPC.2018.03.007