THE GLOBAL WELL-POSEDNESS FOR THE COMPRESSIBLE FLUID MODEL OF KORTEWEG TYPE

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 R-N, 3 <= N <= 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.