Global existence and optimal L2 decay rate for the strong solutions to the compressible fluid models of Korteweg type

In this paper, we consider the compressible Navier–Stokes–Korteweg system that models the motions of the compressible isothermal viscous capillary fluids. We prove the global existence of a strong solution to the compressible Navier–Stokes–Korteweg system when the initial perturbation is small. Furthermore, if the L1 norm of the initial perturbation is finite, we can obtain the optimal L2 decay rates.