@article{43cddc67b26f4d6bbc5d6046117fb2f0,
title = "Existence and uniqueness of solutions to stochastic Rayleigh-Plesset equations",
abstract = "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.",
keywords = "Fluid dynamics, Lyapunov functions, Ordinary differential equations, Stochastic differential equations",
author = "Tadahisa Funaki and Masashi Ohnawa and Yukihito Suzuki and Satoshi Yokoyama",
note = "Funding Information: This work is supported by Japan Society for the Promotion of Science (JSPS) “Construction of mathematical theory to investigate the macro structure and the meso structure of the fluid motion” (KAKENHI, No. 24224004 ) and the Core Research for Evolutional Science and Technology (CREST) of the Japan Science and Technology Agency (JST). The authors thank Professor Hiroaki Yoshimura at Waseda University for several valuable comments. Furthermore, the authors appreciate Professor Yoshihiro Shibata at Waseda University for his kind support. Publisher Copyright: {\textcopyright} 2014 Elsevier Inc.",
year = "2015",
month = may,
day = "1",
doi = "10.1016/j.jmaa.2014.12.018",
language = "English",
volume = "425",
pages = "20--32",
journal = "Journal of Mathematical Analysis and Applications",
issn = "0022-247X",
publisher = "Academic Press Inc.",
number = "1",
}