About the barotropic compressible quantum Navier–Stokes equations. (November 2015)

• Record Type: Journal Article
• Authors: Gisclon, M.; Lacroix-Violet, I.
• Is Part Of: Nonlinear analysis. Volume 128(2015)
• Page Start: 106
• Page End: 121
• Publication Date: 2015-11
• Subjects: 35K35 -- 65N12 -- 76Y05; Quantum Navier–Stokes equations -- Global weak solutions -- Asymptotic analysis; 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.2015.07.006
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper we consider the barotropic compressible quantum Navier–Stokes equations with a linear density dependent viscosity and its limit when the scaled Planck constant vanishes. Following recent works on degenerate compressible Navier–Stokes equations, we prove the global existence of weak solutions by the use of a singular pressure close to vacuum. With such singular pressure, we can use the standard definition of global weak solutions which also allows to justify the limit when the scaled Planck constant denoted by ε tends to 0 .