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.
- Fluid dynamics
- Lyapunov functions
- Ordinary differential equations
- Stochastic differential equations
ASJC Scopus subject areas
- Applied Mathematics