Global solvability of the initial boundary value problem for a model system of one-dimensional equations of polytropic flows of viscous compressible fluid mixtures

TL;DR

This paper proves the global existence and uniqueness of strong solutions for a one-dimensional model of viscous compressible fluid mixtures, without restrictive assumptions on viscosity structure.

Contribution

It establishes the first comprehensive proof of global solvability for this class of polytropic fluid mixture models under minimal viscosity assumptions.

Findings

Proved global existence of strong solutions

Established uniqueness of solutions

No restrictions on viscosity matrix structure

Abstract

We consider the initial boundary value problem for a model system of one-dimensional equations which describe unsteady polytropic motions of a mixture of viscous compressible fluids. We prove the global existence and uniqueness theorem for the strong solution without restrictions on the structure of the viscosity matrix except standard properties of symmetry and positiveness.