Viscous regularization of the Euler equations and entropy principles

TL;DR

This paper explores viscous regularizations of the Euler equations, identifying a unique form compatible with all generalized entropies and satisfying the minimum entropy principle, linking it to Brenner's phenomenological model.

Contribution

It introduces a unique viscous regularization of the Euler equations that aligns with all generalized entropies and the minimum entropy principle, connecting to Brenner's model.

Findings

Identified a unique regularization compatible with all generalized entropies.

Established the regularization satisfies the minimum entropy principle.

Connected the regularization to Brenner's phenomenological model.

Abstract

This paper investigates a general class of viscous regularizations of the compressible Euler equations. A unique regularization is identified that is compatible with all the generalized entropies a la Harten and satisfies the minimum entropy principle. A connection with a recently proposed phenomenological model by H. Brenner is made.