The spherically - symmetric problem of the oscillations of a small gas bubble in the center of a spherical flask filled with a compressible liquid that is excited by small radial displacement of the flask's wall is considered. Two asymptotic solutions have been found for the low Mach number stage. The first one is an asymptotic solution for the field far from the bubble, and it corresponds to linear wave theory. The second one is an asymptotic solution for the boundary layer near the bubble and it corresponds to an incompressible fluid. In the analytical solution of the low Mach number stage matching of these asymptotic solutions is done. A generalization of the Rayleigh Plesset equation for a compressible liquid is given in the form of two ordinary difference differential equations that take into account the pressure waves which are reflecting from the bubble and those that are incident on the bubble from the flask wall. The initial value problem for the initiation of the bubble oscillations due to flask wall excitation and for the evolution of these oscillations was considered. Linear and non-linear periodic bubble oscillations were analyzed analytically, and resonant frequencies were identified. Non-linear resonant and near-resonant solutions for the bubble's non-harmonic oscillations, which are excited by harmonic pressure or velocity oscillations on the flask wall, are obtained.
- Bubble dynamics