# Andrea GiorginiImperial College London | Imperial · Department of Mathematics

Andrea Giorgini

PhD

## About

28

Publications

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376

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## Publications

Publications (28)

We analyze continuous data assimilation by nudging for the 3D Ladyzhenskaya equations. The analysis provides conditions on the spatial resolution of the observed data that guarantee synchronization to the reference solution associated with the observed, spatially coarse data. This synchronization holds even though it is not known whether the refere...

We study an initial-boundary value problem for the incompressible Navier-Stokes-Cahn-Hilliard system with non-constant density proposed by Abels, Garcke and Gr\"{u}n in 2012. This model arises in the diffuse interface theory for binary mixtures of viscous incompressible fluids. This system is a generalization of the well-known model H in the case o...

We derive a novel thermodynamically consistent Navier--Stokes--Cahn--Hilliard system with dynamic boundary conditions. This model describes the motion of viscous incompressible binary fluids with different densities. In contrast to previous models in the literature, our new model allows for surface diffusion, a variable contact angle between the di...

This paper is devoted to the global well-posedness of two Diffuse Interface systems modeling the motion of an incompressible two-phase fluid mixture in presence of capillarity effects in a bounded smooth domain Ω⊂Rd, d=2,3. We focus on dissipative mixing effects originating from the mass-conserving Allen-Cahn dynamics with the physically relevant F...

\bfA \bfb \bfs \bft \bfr \bfa \bfc \bft . We study a diffuse interface model describing the evolution of the flow of a binary fluid in a Hele-Shaw cell. The model consists of a Cahn-Hilliard-Darcy type system with transport and mass source. A relevant physical application is related to tumor growth dynamics, which in particular justifies the occurr...

We study the separation property for Cahn-Hilliard type equations with constant mobility and (physically relevant) singular potentials in two dimensions. That is, the solutions, with initial finite energy, stay uniformly away from the pure phases ±1 from a certain time on. Beyond its physical interest, this property plays a crucial role to achieve...

We investigate the longtime behavior of the solutions to the Navier-Stokes-Cahn-Hilliard system (also known as Model H) with singular (e.g. Flory-Huggins) potential and non-constant viscosity. We prove that the initial and boundary value problem generates a strongly continuous semigroup on a suitable phase-space. Next, we establish the existence of...

This work is devoted to the analysis of strong solutions to the Abels-Garcke-Gr\"{u}n (AGG) model in three dimensions. First, we prove the existence of local-in-time strong solutions originating from an initial datum $(\mathbf{u}_0, \phi_0)\in \mathbf{H}^1_\sigma \times H^2(\Omega)$ such that $\mu_0 \in H^1(\Omega)$ and $|\overline{\phi_0}|\leq 1$....

We analyze continuous data assimilation by nudging for the 3D Ladyzhenskaya equations. The analysis provides conditions on the spatial resolution of the observed data that guarantee synchronization to the reference solution associated with the observed, spatially coarse data. This synchronization holds even though it is not known whether the refere...

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 p...

We study a diffuse interface model describing the evolution of the flow of a binary fluid in a Hele-Shaw cell. The model consists of a Cahn-Hilliard-Darcy (CHD) type system with transport and mass source. A relevant physical application is related to tumor growth dynamics, which in particular justifies the occurrence of a mass inflow. We study the...

We study the nonhomogeneous incompressible Navier-Stokes-Cahn-Hilliard system in a bounded smooth domain in Rd, d=2,3. This model arises from the Diffuse Interface theory of binary mixtures accounting for density variation, capillarity effects at the interface and partial mixing. We consider the case of initial density away from zero and concentrat...

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 p...

This paper is devoted to the mathematical analysis of some Diffuse Interface systems which model the motion of a two-phase incompressible fluid mixture in presence of capillarity effects in a bounded smooth domain. First, we consider a two-fluids parabolic-hyperbolic model that accounts for unmatched densities and viscosities without diffusive dyna...

We study a diffuse interface model describing the motion of two viscous fluids driven by 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...

This paper addresses the well-posedness of a diffuse interface model for the motion of binary fluids with different viscosities. The system consists of the Brinkman–Darcy law governing the fluid velocity, nonlinearly coupled with a convective Cahn–Hilliard equation for the difference of the fluid concentrations. In a three-dimensional bounded domai...

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 en...

The motion of two contiguous incompressible and viscous fluids is described within the diffuse interface theory by the so-called Model H. The system consists of the Navier-Stokes equations, which are coupled with the Cahn-Hilliard equation associated to the Ginzburg-Landau free energy with physically relevant logarithmic potential. This model is st...

We study a diffuse interface model of the two-component Hele–Shaw flow. This is an advective Cahn–Hilliard equation for the relative concentration , where the incompressible velocity field is determined by the Darcy's law depending on the Korteweg force . Here μ is the derivative of a nonlocal non-convex free energy characterized by a logarithmic p...

The Cahn–Hilliard–Hele–Shaw system is a fundamental diffuse-interface model for an incompressible binary fluid confined in a Hele–Shaw cell. It consists of a convective Cahn–Hilliard equation in which the velocity u is subject to a Korteweg force through Darcy's equation. In this paper, we aim to investigate the system with a physically relevant po...

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 Tach...

This paper is focused on a diffuse interface model for the motion of binary fluids with different viscosities. The system consists of the Brinkman-Darcy equations governing the fluid velocity, nonlinearly coupled with a convective Cahn-Hilliard equation for the difference of the fluid concentrations. For the three-dimensional Cahn-Hilliard-Brinkman...

We consider the so-called Cahn-Hilliard-Oono equation with singular (e.g. logarithmic) potential in a bounded domain of Rd, d ≤ 3. The equation is subject to an initial condition and Neumann homogeneous boundary conditions for the order parameter as well as for the chemical potential. However, contrary to the Cahn-Hilliard equation, the total mass...

We consider the nonlocal Cahn-Hilliard equation with singular potential and constant mobility. Well-posedness and regularity of weak solutions are studied. Then we establish the validity of the separation property in dimension two. Further regularity results as well as the existence of regular finite dimensional attractors and the convergence of a...

We propose a mathematical analysis of the Swift-Hohenberg equation arising from the phase field theory to model the transition from an unstable to a (meta)stable state. We also consider a recent generalization of the original equation, obtained by introducing an inertial term, to predict fast degrees of freedom in the system. We formulate and prove...

Phase-field crystal models are used to describe several pattern formation phenomena like crystallization of liquid, diffusion defects and glass formation. The prototypical equation is obtained as the conserved gradient flow associated with a free-energy functional of Swift-Hohenberg type. Here we consider a variant of the phase-field crystal equati...

## Projects

Projects (2)

To model and solve problems in fluid dynamics that involve two-phase flows, etc.

Nonlinear initial and boundary value problems involving fractional diffusion operators and/or other nonlocal operators. In particular, with applications in phase transition phenomena and transmission problems with internal Lipschitz boundaries.