Global Solutions of an Initial Boundary Value Problem for the Euler-Poisson-Korteweg System
Xian Zhang *
School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, Guangdong, PR China.
*Author to whom correspondence should be addressed.
Abstract
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.
Keywords: Energy estimates, Euler-Poisson-Korteweg System, Global existence