Time periodic solutions of compressible fluid models of Korteweg type

TL;DR

This paper investigates the existence, uniqueness, and stability of time-periodic solutions for the compressible Navier-Stokes-Korteweg system under periodic external forces, using energy methods and decay estimates.

Contribution

It establishes the conditions for time-periodic solutions and their stability, extending understanding of fluid models with capillarity effects under periodic forcing.

Findings

Proves existence of time-periodic solutions.

Shows stability and decay rates of solutions.

Provides conditions for uniqueness and asymptotic behavior.

Abstract

This paper is concerned with the existence, uniqueness and time-asymptotic stability of time periodic solutions to the compressible Navier-Stokes-Korteweg system effected by a time periodic external force in $\mathbb{R}^n$. Our analysis is based on a combination of the energy method and the time decay estimates of solutions to the linearized system.