Long-time behavior of solution for the compressible Navier–Stokes–Korteweg equations in R3

Abstract In this paper, we study the long-time behavior of solution for the compressible Navier–Stokes–Korteweg equations in three-dimensional whole space. More precisely, we focus on establishing the optimal time decay rates for the higher-order spatial derivatives of density and velocity, which will improve the work of Wang and Tan (2011).