On the compactness of weak solutions to the Navier–Stokes–Korteweg equations for capillary fluids. (October 2019)

• Record Type: Journal Article
• Authors: Antonelli, Paolo; Spirito, Stefano
• Is Part Of: Nonlinear analysis. Volume 187(2019)
• Page Start: 110
• Page End: 124
• Publication Date: 2019-10
• Subjects: primary 35Q35 -- secondary 35D05 76N10; Compressible fluids -- Navier–Stokes–Korteweg -- Capillarity -- Vacuum -- Compactness; 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.2019.03.020
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper we consider the Navier–Stokes–Korteweg equations for a viscous compressible fluid with capillarity effects in three space dimensions. We prove compactness of finite energy weak solutions for large initial data. Incontrast with previous results regarding this system, vacuum regions are allowed in the definition of weak solutions and no additional damping terms are considered. The compactness is obtained by introducing suitable truncations of the velocity field and the mass density at different scales and use only the a priori bounds obtained by the energy and the BD entropy.