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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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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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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DOI: https://doi.org/10.1007/978-3-0348-0939-9_22
Publisher Name: Birkhäuser, Basel
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