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Recent Developments of Mathematical Fluid Mechanics pp 411–442Cite as

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On Incompressible Two-Phase Flows with Phase Transitions and Variable Surface Tension

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Part of the book series: Advances in Mathematical Fluid Mechanics ((AMFM))

Abstract

Our study of the basic model for incompressible two-phase flows with phase transitions consistent with thermodynamics (Prüss et al., Evol Equ Control Theory 1:171–194, 2012; Prüss and Shimizu, J Evol Equ 12:917–941, 2012; Prüss et al., Commun Part Differ Equ 39:1236–1283, 2014; see also Prüss et al., Interfaces Free Bound 15:405–428, 2013) is extended to the case of temperature-dependent surface tension. We prove well-posedness in an L p -setting, study the stability of the equilibria of the problem, and show that a solution which does not develop singularities exists globally, and if its limit set contains a stable equilibrium it converges to this equilibrium in the natural state manifold for the problem as time goes to infinity.

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References

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Acknowledgements

The work of SS was partially supported by JSPS Grant-in-Aid for Scientific Research (B) #24340025 and Challenging Exploratory Research #23654048. The work of GS was partially supported by a grant from the Simons Foundation (#245959) and by a grant from NSF (DMS-1265579).

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Authors and Affiliations

  1. Institut für Mathematik, Martin-Luther-Universität Halle-Wittenberg, 06099, Halle, Germany

    Jan Prüss & Mathias Wilke

  2. Graduate School of Human and Environmental Studies, Kyoto University, Kyoto, 606-8501, Japan

    Senjo Shimizu

  3. Department of Mathematics, Vanderbilt University, Nashville, TN, 37240, USA

    Gieri Simonett

Authors
  1. Jan Prüss
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  2. Senjo Shimizu
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  3. Gieri Simonett
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  4. Mathias Wilke
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Corresponding author

Correspondence to Jan Prüss .

Editor information

Editors and Affiliations

  1. Universität of Zürich, Institut für Mathematik, Zürich, Switzerland

    Herbert Amann

  2. University of Tokyo, Graduate School of Mathematical Sciences, Tokyo, Japan

    Yoshikazu Giga

  3. Department of Mathematics, Waseda University, Tokyo, Japan

    Hideo Kozono

  4. Research Institute for Mathematical Sciences, Kyoto University Kitashirakawa, Kyoto, Japan

    Hisashi Okamoto

  5. Department of Mathematics, Waseda University, Tokyo, Japan

    Masao Yamazaki

Additional information

Dedicated to Professor Yoshihro Shibata on the occasion of his 60th anniversary

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Prüss, J., Shimizu, S., Simonett, G., Wilke, M. (2016). On Incompressible Two-Phase Flows with Phase Transitions and Variable Surface Tension. In: Amann, H., Giga, Y., Kozono, H., Okamoto, H., Yamazaki, M. (eds) Recent Developments of Mathematical Fluid Mechanics. Advances in Mathematical Fluid Mechanics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0939-9_22

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