, Volume 64, Issue 4, pp 1161-1176
Date: 17 Nov 2012

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

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Abstract

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.

Project 10901107 was supported by National Natural Science Foundation of China. Project 11101076 was supported by National Natural Science Foundation of China. This study was supported by Innovation Program of Shanghai Municipal Education Commission.