Zeitschrift für angewandte Mathematik und Physik

, Volume 64, Issue 4, pp 1161-1176

First online:

Stability of non-isothermal phase transitions in a steady van der Waals flow

  • Shu-Yi ZhangAffiliated withBusiness Information Management School, Shanghai Institute of Foreign Trade Email author 

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This paper is concerned with the multidimensional stability of non-isothermal subsonic phase transitions in a steady supersonic flow of van der Waals type. For the sake of seeking physical admissible planar waves, the viscosity–capillarity criterion (Slemrod in Arch Ration Mech Anal 81(4):301–315, 1983) is chosen to be the admissible criterion. By showing the Lopatinski determinant being non-zero, we prove that subsonic phase transitions are uniformly stable in the sense of Majda (Mem Am Math Soc 41(275):1–95, 1983) under both one-dimensional and multidimensional perturbations.


Supersonic flows Non-isothermal subsonic phase transitions Euler equations Multidimensional stability

Mathematics Subject Classification (2010)

35L65 35L67