Abstract
We consider the compressible Navier–Stokes–Korteweg system that models the motions of the compressible isothermal viscous capillary fluids. We prove the optimal L2 and Lp, p⩾2 decay rates for the classical solutions and their spatial derivatives. In particular, the optimal L2 decay rate of the second-order spatial derivatives is obtained. The proof is based on the detailed study of the linear decay estimates and nonlinear energy estimates.
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