The theory of formation, growth and collapse of gas bubbles (gas cavitation) was first developed for the incompressible ideal fluid for the case of a single spherical bubble. The equations of bubble dynamics were then modified to account for the compressibility, viscosity, and heat conductivity, as well as finiteness of the amplitude of oscillations of a bubble wall. Finally, this theory took into account non-spherical bubble oscillations, especially near its resonance frequencies and at rather large sound amplitudes. It was shown that non-spherical oscillations and the liquid jets appearing near the collapsing bubbles, if they are located in the proximity of a solid surface, cause cavitation erosion of solid bodies. Later, theoretical studies were performed as applied to the dynamics of vapor bubbles (vapor cavitation), which has a lot in common with a gas bubble, but there are certain significant differences.
Most of the theoretical works are devoted to the theory of motion of a single bubble, whereas a combination of a large number of interacting bubbles of different sizes is usually considered in the experimental studies.