The Global Well-Posedness for the Compressible Fluid Model of Korteweg Type

Abstract

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 ${\Bbb R}^N$, $3\leq N \leq 7$. 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.