On the relaxation towards mechanical equilibrium for two-pressure compressible flows

TL;DR

This paper introduces a symmetrized two-pressure compressible flow model that justifies the zero viscosity limit, recovers the Kapila model, and demonstrates a pressure-driven stabilization mechanism leading to global solutions.

Contribution

It presents a new symmetrization of a two-pressure model, enabling analysis of the zero viscosity limit and stability properties not previously established.

Findings

Justifies the zero compaction viscosity limit.

Recovers solutions of the Kapila model.

Establishes a pressure-induced stabilization mechanism.

Abstract

We introduce a symmetrization of a one-velocity two-pressures Baer-Nunziato type model for mixtures of barotropic compressible fluids. It allows us to justify the zero compaction viscosity limit and to recover a solution of the so-called Kapila model. On the other hand, the symmetrization highlights a pressure-induced stabilization mechanism which allows us to recover a global-in-time existence result for initial data close to constant states.