# Galilean invariance and entropy principle for a system of balance laws of mixture type

### Takashi Arima

Kanagawa University, Yokohama, Japan### Tommaso Ruggeri

Università di Bologna, Italy### Masaru Sugiyama

Nagoya Institute of Technology, Japan### Shigeru Taniguchi

National Institute of Technology, Kitakyushu College, Kitakyushu, Japan

## Abstract

After defining, in analogy with a mixture of continuous media, a *system of balance laws of mixture type*, we study the general properties obtained by imposing the Galilean invariance principle. For constitutive equations of local type we study also the entropy principle and we prove the compatibility between the two principles. These general results permit us to construct, from a single constituent theory, the corresponding theory of mixtures in an easy way. As an illustrative example of the general theory, we write down the hyperbolic system of balance laws of mixtures in which each component has 6 fields (mass density, velocity, temperature and dynamic pressure, among which only the last one is a nonequilibrium variable). This is the simplest system after Eulerian mixtures. Global existence of smooth solutions for small initial data is also proved.

## Cite this article

Takashi Arima, Tommaso Ruggeri, Masaru Sugiyama, Shigeru Taniguchi, Galilean invariance and entropy principle for a system of balance laws of mixture type. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 28 (2017), no. 3, pp. 495–513

DOI 10.4171/RLM/773