Abstract
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 ‖ρ0−ρ¯‖H2+‖u0‖H1 is small. Furthermore, if the L1 norm of the initial perturbation is finite, we can obtain the optimal L2 decay rates.
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