Abstract
The basic model for incompressible two-phase flows with phase transitions consistent with thermodynamics is studied. The latter means that the total energy is conserved and the total entropy is nondecreasing. We consider the case of constant but non-equal densities of the phases, complementing our previous paper (Prüss et al. in Evol Equ Control Theory 1:171–194, 2012) where the case of equal densities is analyzed. The local well-posedness of such problems is proved by means of the technique of maximal L p -regularity, in a configuration where the interface is nearly flat and initial data are small.
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Dedicated to Yoshihiro Shibata on the ocasion of his 60th anniversary.
S.S. expresses her thanks for hospitality to the Institute of Mathematics, Martin-Luther-Universität Halle-Wittenberg, where important parts of this work originated. The research of S.S was partially supported by JSPS Grant-in-Aid for Scientific Research (B)—24340025 and Challenging Exploratory Research—23654048, MEXT.
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Prüss, J., Shimizu, S. On well-posedness of incompressible two-phase flows with phase transitions: the case of non-equal densities. J. Evol. Equ. 12, 917–941 (2012). https://doi.org/10.1007/s00028-012-0161-3
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DOI: https://doi.org/10.1007/s00028-012-0161-3