The existence of global strong solutions to a multi-dimensional compressible Navier-Stokes-Poisson-Korteweg system with some large initial data

This article is concerned with the Cauchy problem to a multi-dimensional compressible Navier-Stokes-Poisson-Korteweg model. We prove the global existence of strong solution to the model with some large initial data. Moreover, we also present an example to explain that this kind of initial data satisfy some smallness condition, while the norms of each component are arbitrarily large in critical Besov spaces.