Global solutions for the compressible quantum hydrodynamic model in a bounded domain. (July 2019)

• Record Type: Journal Article
• Authors: Pu, Xueke; Li, Min
• Is Part Of: Nonlinear analysis. Volume 184(2019)
• Page Start: 148
• Page End: 171
• Publication Date: 2019-07
• Subjects: 76Y05 -- 35G31 -- 35A01 -- 35B45; Full quantum hydrodynamic model -- Initial boundary value problem -- Global smooth solutions -- Energy estimates; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.01.029
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: 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.