Existence and uniqueness of solutions to stochastic Rayleigh-Plesset equations

Tadahisa Funaki, Masashi Ohnawa, Yukihito Suzuki, Satoshi Yokoyama

Research output: Contribution to journalArticle

3 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)20-32
Number of pages13
JournalJournal of Mathematical Analysis and Applications
Volume425
Issue number1
DOIs
Publication statusPublished - 2015 May 1

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Rayleigh Equation
Lyapunov functions
Existence and Uniqueness of Solutions
Stochastic Equations
Invariant Measure
Global Solution
Lyapunov Function
Bubble
Water
Motion
Term

Keywords

  • Fluid dynamics
  • Lyapunov functions
  • Ordinary differential equations
  • Stochastic differential equations

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Existence and uniqueness of solutions to stochastic Rayleigh-Plesset equations. / Funaki, Tadahisa; Ohnawa, Masashi; Suzuki, Yukihito; Yokoyama, Satoshi.

In: Journal of Mathematical Analysis and Applications, Vol. 425, No. 1, 01.05.2015, p. 20-32.

Research output: Contribution to journalArticle

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