Global Solutions of an Initial Boundary Value Problem for the Euler-Poisson-Korteweg System

The Euler-Poisson-Korteweg system is a mathematical model arising from hydrodynamics and quantum hydrodynamics. It can be used to describe at interface the ow of capillary ows, such as the liquid-vapor mixture. In this paper, we obtain the global existence of solutions for high-dimensional compressible Euler-Poisson-Korteweg systems with small initial values by the energy method. The study can provide a theoretical basis for the development of efficient numerical solution methods, as well as contribute to the further study of other properties of the solution such as vibrational and bursting properties.