Asymptotic Stability of Solutions for 1-D Compressible Navier-Stokes-Cahn-Hilliard system

TL;DR

This paper investigates the long-term behavior of solutions to a 1-D compressible Navier-Stokes-Cahn-Hilliard system, proving asymptotic stability and analyzing how initial concentration differences influence interface evolution.

Contribution

It establishes the global existence and asymptotic stability of strong solutions for the 1-D compressible Navier-Stokes-Cahn-Hilliard system under large initial disturbances.

Findings

Solutions are asymptotically stable over time.

Initial concentration difference affects interface behavior.

Stability holds even with large initial disturbances.

Abstract

This paper is concerned with the evolution of the periodic boundary value problem and the mixed boundary value problem for a compressible mixture of binary fluids modeled by the Navier-Stokes-Cahn-Hilliard system in one dimensional space. The global existence and the large time behavior of the strong solutions for these two systems are studied. The solutions are proved to be asymptotically stable even for the large initial disturbance of the density and the large velocity data. We show that the average concentration difference for the two components of the initial state determines the long time behavior of the diffusive interface for the two-phase flow.