arXiv subjects

Andrea Giorgini

Publications and source records attributed to Andrea Giorgini.

21 records · Page 2Linked to original sources

arXiv2020

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

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.

math.AP↗

arXiv2019

Well-posedness of a diffuse interface model for Hele-Shaw flows

We study a diffuse interface model describing the motion of two viscous fluids driven by the surface tension in a Hele-Shaw cell. The full system consists of the Cahn-Hilliard equation coupled with the Darcy's law. We address the physically relevant case in which the two fluids have different viscosities (unmatched viscosities case) and the free energy density is the logarithmic Helmholtz potential. In dimension two we prove the uniqueness of weak solutions under a regularity criterion, and the existence and uniqueness of global strong solutions. In dimension three we show the existence and uniqueness of strong solutions, which are local in time for large data or global in time for appropriate small data. These results extend the analysis obtained in the matched viscosities case by Giorgini, Grasselli and Wu (Ann. Inst. H. Poincaré Anal. Non Linéaire 35 (2018), 318-360). Furthermore, we prove the uniqueness of weak solutions in dimension two by taking the well-known polynomial approximation of the logarithmic potential.

math.AP↗

arXiv2017

Navier-Stokes-Voigt equations with memory in 3D lacking instantaneous kinematic viscosity

We consider a Navier-Stokes-Voigt fluid model where the instantaneous kinematic viscosity has been completely replaced by a memory term incorporating hereditary effects, in presence of Ekman damping. The dissipative character of our model is weaker than the one where hereditary and instantaneous viscosity coexist, previously studied by Gal and Tachim-Medjo. Nevertheless, we prove the existence of a regular exponential attractor of finite fractal dimension under rather sharp assumptions on the memory kernel.

math.AP↗