  In this paper, we consider the compressible fluid model of Korteweg type
which can be used as a phase transition model. It is shown that the system
admits a unique, global strong solution for small initial data in $\mathbb
R^N$, $N \geq 3$. In this study, the main tools are the maximal $L_p$-$L_q$
regularity and $L_p$-$L_q$ decay properties of solutions to the linearized
equations.
