A minimum entropy principle in the compressible multicomponent Euler equations

Abstract

In this work, the space of admissible entropy functions for the compressible multicomponent Euler equations is explored, following up on [Harten, \textit{J. Comput. Phys.}, 49 (1), 1983, pp. 151-164]. This effort allows us to prove a minimum entropy principle on entropy solutions, whether smooth or discrete, in the same way it was originally demonstrated for the compressible Euler equations by [Tadmor, \textit{Appl. Numer. Math.}, 49 (3-5), 1986, pp. 211-219].