Global solutions for the compressible quantum hydrodynamic model in a bounded domain

This paper concerns the existence of global smooth solutions to the initial boundary value problem for a three-dimensional compressible quantum hydrodynamic model with damping and heat diffusion in a bounded domain in R-3. Based on the continuation argument and the uniform a priori estimates with respect to the time, we obtain the existence of global solutions in a bounded smooth domain provided that the initial perturbation around a constant state is small enough. The key difficulty is to deal with the higher order quantum terms, which do play an essential role in establishing the a priori estimates. The boundary conditions finally adopted are the insulating boundary conditions. (C) 2019 Elsevier Ltd. All rights reserved.