Evaluation of the Lopatinski condition for gas dynamics
Published in Handbook of Mathematical Fluid Dynamics III, 2004
Recommended citation: H. Kristian Jenssen & Gregory Lyng, Evaluation of the Lopatinski condition for gas dynamics, appendix to K. Zumbrun, Stability of large-amplitude shock waves of compressible Navier–Stokes equations, Handbook of Mathematical Fluid Dynamics III, S. Friedlander & D. Serre eds., North-Holland, Amsterdam, 2004.
The purpose of this appendix is to calculate the Lopatinski determinant, or “stability function,” for the Euler equations of compressible gas dynamics. We describe two approaches to this problem. In the first we use a change of variables to simplify the computation. In the second method we take advantage of the Galilean invariance of the Euler equations and exploit a relationship between the eigenvectors of a particular pair of matrices. As a preliminary step for the first technique, we discuss how the Lopatinski determinant behaves under a change of coordinates.
Recommended citation: H. Kristian Jenssen & Gregory Lyng, Evaluation of the Lopatinski condition for gas dynamics, appendix to K. Zumbrun, Stability of large-amplitude shock waves of compressible Navier–Stokes equations, Handbook of Mathematical Fluid Dynamics III, S. Friedlander & D. Serre eds., North-Holland, Amsterdam, 2004.