Stability of multidimensional phase transitions in a steady van der Waals flow

Abstract

In this paper, the author studies the multidimensional stability of subsonic phase transitions in a steady supersonic flow of van der Waals type. The viscosity capillarity criterion (in “Arch. Rat. Mech. Anal., 81(4), 1983, 301–315”) is used to seek physical admissible planar waves. By showing the Lopatinski determinant being non-zero, it is proved that subsonic phase transitions are uniformly stable in the sense of Majda (in “Mem. Amer. Math. Soc., 41(275), 1983, 1–95”) under both one dimensional and multidimensional perturbations.

Keywords

Supersonic flows / Subsonic phase transitions / Euler equations / Multi-dimensional stability

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