Analysis of a thermodynamically consistent Navier–Stokes–Cahn–Hilliard model. (December 2021)

• Record Type: Journal Article
• Authors: Lasarzik, Robert
• Is Part Of: Nonlinear analysis. Volume 213(2021)
• Publication Date: 2021-12
• Subjects: 35Q35 -- 35D99 -- 76D05; Weak–strong uniqueness -- Phase transition -- Navier–Stokes -- Cahn–Hilliard -- Existence -- Thermodynamical consistent -- Dissipative solutions -- Relative energy; 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.2021.112526
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, existence of generalized solutions to a thermodynamically consistent Navier–Stokes–Cahn–Hilliard model introduced in Eleuteri et al. (2015) is proven in any space dimension. The generalized solvability concepts are measure-valued and dissipative solutions. The measure-valued formulation incorporates an entropy inequality and an energy inequality instead of an energy balance in a nowadays standard way, the Gradient flow of the internal variable is fulfilled in a weak and the momentum balance in a measure-valued sense. In the dissipative formulation, the distributional relations of the momentum balance and the energy as well as entropy inequality are replaced by a relative energy inequality. Additionally, we prove the weak–strong uniqueness of the proposed solution concepts and that all generalized solutions with additional regularity are indeed strong solutions.