Global unique solvability of the initial-boundary value problem for the equations of one-dimensional polytropic flows of viscous compressible multifluids

TL;DR

This paper proves the global existence and uniqueness of solutions for the initial-boundary value problem describing one-dimensional viscous compressible multifluid flows with polytropic behavior.

Contribution

It establishes the first rigorous proof of global solvability for these complex multifluid flow equations under initial-boundary conditions.

Findings

Global existence of solutions is proven.

Uniqueness of solutions is established.

Results apply to flows in bounded domains.

Abstract

We consider the equations which describe polytropic one-dimensional flows of viscous compressible multifluids. We prove global existence and uniqueness of a solution to the initial-boundary value problem which corresponds to the flow in a bounded space domain.