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A Diffuse Interface Model of a Two-Phase Flow with Thermal Fluctuations

  • Eduard Feireisl
  • Madalina PetcuEmail author
Article

Abstract

We consider a model of a two phase flow proposed by Anderson et al. taking into account possible thermal fluctuations. The mathematical model consists of the compressible Navier–Stokes system coupled with the Cahn–Hilliard equation, where the latter is driven by a multiplicative temporal white noise accounting for thermal fluctuations. We show existence of dissipative martingale solutions satisfying the associated total energy balance.

Keywords

Compressible Navier–Stokes system Stochastic Cahn–Hilliard equation Weak martingale solution 

Notes

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute of Mathematics of the Academy of Sciences of the Czech RepublicPraha 1Czech Republic
  2. 2.Technical University Berlin, Institute of MathematicsBerlinGermany
  3. 3.Laboratoire de Mathématiques et ApplicationsUMR CNRS 7348 - SP2MI Université de PoitiersFuturoscope CedexFrance
  4. 4.The Institute of Mathematics of the Romanian AcademyBucharestRomania
  5. 5.The Institute of Statistics and Applied Mathematics of the Romanian AcademyBucharestRomania

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