  The Minneart resonance is a low frequency resonance in which the wavelength
is much larger than the size of the resonators. It is interesting to study the
interaction between two adjacent bubbles when they are brought close together.
Because the bubbles are usually compressible, in this paper we mainly
investigate resonant modes of two general convex resonators with arbitrary
shapes to extend the results of Ammari, Davies, Yu in [4], where a pair of
spherical resonators are considered by using bispherical coordinates. We
combine the layer potential method for Helmholtz equation in [4,5] and the
elliptic theory for gradient estimates in [26,30] to calculate the capacitance
coefficients for the coupled $C^{2,\alpha}$ resonators, then show the
leading-order asymptotic behaviors of two different resonant modes and reveal
the dependance of the resonant frequencies on their geometric properties, such
as convexity, volumes and curvatures. By the way, the blow-up rates of gradient
of the scattered pressure are also presented.
