Existence of solutions for a viscous hybrid quantum system for arbitrary large current density. (October 2022)

• Record Type: Journal Article
• Authors: Di Michele, Federica; Rubino, Bruno; Sampalmieri, Rosella
• Other Names: Bersani Alberto Maria guest-editor.; Cazzani Antonio M guest-editor.; Eremeyev Victor guest-editor.; Giorgio Ivan guest-editor.; Spagnuolo Mario guest-editor.
• Is Part Of: Mathematics and mechanics of solids. Volume 27:Number 10(2022)
• Page Start: 2189
• Page End: 2200
• Publication Date: 2022-10
• Subjects: Hybrid quantum hydrodynamic model -- viscosity -- stationary solutions -- hybrid limit -- regularity of solution; Materials -- Mechanical properties -- Periodicals; Solids -- Periodicals; Materials science -- Mathematics -- Periodicals; 620.11205
• DOI: 10.1177/10812865221105812
• Languages: English
• ISSNs: 1081-2865

Abstract

In this paper, we continue to analyse the properties of the hybrid model introduced in the works by Chiarelli et al. and Di Michele et al. In particular, we consider a quantum hybrid model with a special viscous functional, as introduced in the work by Gamba and Jüngel, for the quantum hydrodynamical model in its standard form (QHD). We show that the hybrid QHD (H-QHD) model admits weak solutions also for arbitrary large value of the current density J under a suitable pressure function.