Biro Computer and Automation Institute, Hungarian Academy of Sciences 1. Our research is encouraged by the so called sonoluminescence phenomenon which is discovered by Fremzel and Schultes in 1934. The term refers to the fact that gas bubbles in a fluid may emit light while undergoing wildly nonlinear oscillations under the effect of an external sound field. Consider for the sake of simplicity the case of a single, radially symmetric gas bubble in water which occupies a container on which an oscillatory acoustic field is applied.
External oscillations give alternatively rise to the expansion and compression of the bubble.
When the acoustic field is in antiphase, a negative relative pressure acts on the bubble, whose radius expands while the bubble absorbs energy from the medium. However, as a maximum of the external field is approached, the bubble starts to shrink, and the compressional portion of the imposed sound field causes the bubble to collapse in a runaway fashion. While a large amount of experimental data on sonoluminescence is now available, no theory seems to exist that can account for the evolution of the bubble radius and the intensity of the emitted light. The dynamics of sonoluminescence appears to be at the same time rich and involved. In this work we shall concentrate in the hydrodynamic regime of the problem, which is expected to describe the motion until a first emission of light occurs.