Existence and uniqueness of solutions to stochastic Rayleigh–Plesset equations

The goal of the present paper is to establish a mathematical basis for analyses of the Rayleigh–Plesset equation combined with certain types of stochastic terms for studying motions of a single bubble immersed in water. We show the unique existence of global solutions to the system and also the existence of invariant measures making use of a suitable Lyapunov function constructed for the underlying deterministic dynamics.