Well-posedness of the two-dimensional Abels–Garcke–Grun model for two-phase flows with unmatched densities

Andrea Giorgini

2021Virtual Community of Pathological Anatomy (University of Castilla La Mancha)25 citationsDOI Open Access PDF

Abstract

We study the Abels–Garcke–Grün (AGG) model for a mixture of two viscous incompressible fluids with different densities. The AGG model consists of a Navier–Stokes–Cahn–Hilliard system characterized by a (non-constant) concentration-dependent density and an additional flux term due to interface diffusion. In this paper we address the well-posedness problem in the two-dimensional case. We first prove the existence of local strong solutions in general bounded domains. In the space periodic setting we show that the strong solutions exist globally in time. In both cases we prove the uniqueness and the continuous dependence on the initial data of the strong solutions. Lastly, we show a stability result for the strong solutions to the AGG model and the model H in terms of the density values.

Topics & Concepts

MathematicsUniquenessBounded functionCompressibilityConstant (computer programming)Stability (learning theory)DiffusionMathematical analysisSpace (punctuation)Flux (metallurgy)Phase (matter)Mathematical physicsThermodynamicsPhysicsChemistryLinguisticsQuantum mechanicsMachine learningProgramming languageOrganic chemistryPhilosophyComputer scienceSolidification and crystal growth phenomenaAdvanced Mathematical Modeling in EngineeringNavier-Stokes equation solutions