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

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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.

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Notes

  1. Here and in all that follows, we denote the weak limit of nonlinear terms by the pointwise limit under the bar sign.

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Authors and Affiliations

  1. Institute of Mathematics of the Academy of Sciences of the Czech Republic, Žitná 25, 115 67, Praha 1, Czech Republic

    Eduard Feireisl

  2. Technical University Berlin, Institute of Mathematics, Strasse des 17. Juni 136, 10623, Berlin, Germany

    Eduard Feireisl

  3. Laboratoire de Mathématiques et Applications, UMR CNRS 7348 - SP2MI Université de Poitiers, Boulevard Marie et Pierre Curie - Téléport 2, 86962, Futuroscope Cedex, Chasseneuil, France

    Madalina Petcu

  4. The Institute of Mathematics of the Romanian Academy, Bucharest, Romania

    Madalina Petcu

  5. The Institute of Statistics and Applied Mathematics of the Romanian Academy, Bucharest, Romania

    Madalina Petcu

Authors
  1. Eduard Feireisl
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  2. Madalina Petcu
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Correspondence to Madalina Petcu.

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The research of E.F. leading to these results has received funding from the Czech Sciences Foundation (GAČR), Grant Agreement 18-05974S. The Institute of Mathematics of the Academy of Sciences of the Czech Republic is supported by RVO:67985840.

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Feireisl, E., Petcu, M. A Diffuse Interface Model of a Two-Phase Flow with Thermal Fluctuations. Appl Math Optim 83, 531–563 (2021). https://doi.org/10.1007/s00245-019-09557-2

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