Abstract
In this paper, we consider the initial value problem for the compressible fluid models of Korteweg type in $${\mathbb {R}}^n(n\ge 3)$$ and asymptotic profile of global solutions and the corresponding convergence rate are established. The structure of the nonlinear term plays a very important role in constructing asymptotic profile. The proof is based on the decay estimate of solutions operator, decay estimate and weighted decay estimate of global solutions.
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