Stability of Multidimensional Phase Transitions in a Steady van der Waals Flow

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 cap- illarity 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.