Time periodic solutions of compressible fluid models of Korteweg type
  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. 
Zhengzheng Chen, Qinghua Xiao, Huijiang Zhao
math.AP