A. Poiatti

Thermal Transmission in a Film-Bulk Domain: Finite-Thickness Film and Thin-Film Limit

Ferdinando Auricchio, Mihaela Chiappetta, Andrea Poiatti +1

We investigate a thermal transmission problem in a domain composed of a film region and a bulk region coupled through an interface where temperature continuity and heat-flux balanc…

Global weak varifold solutions to Navier-Stokes/Mean Curvature Flow system

Andrea Poiatti

The Navier-Stokes/Mean Curvature Flow system describes a two-phase flow of incompressible, viscous and immiscible fluids separated by a sharp interface, whose evolution is governed…

De Giorgi varifold solutions to Mean Curvature Flow: a minimizing movements approach

Tim Laux, Andrea Poiatti

We propose an alternative existence proof of global weak solutions to mean curvature flow and volume preserving mean curvature flow. We prove for the first time for a minimizing mo…

Weak and strong solutions for a class of quasilinear Allen--Cahn systems

Harald Garcke, Tim Laux, Andrea Poiatti

We consider a quasilinear Allen--Cahn system which arises when the gradient energy term in the Ginzburg--Landau energy also contains zero order terms. Such systems offer significan…

Well-posedness and longtime behavior of the conserved Navier--Stokes--Allen--Cahn equations with unmatched viscosities and singular potential

Maurizio Grasselli, Christoph Hurm, Andrea Poiatti

We consider an incompressible Navier--Stokes system nonlinearly coupled with a conserved Allen--Cahn equation with a singular potential (e.g., of Flory--Huggins type). This model d…

math.NA2026

Singularities in phase separation models: a spectral element approach for the nonlocal Cahn-Hilliard equation

Andrés Miniguano-Trujillo, Andrea Poiatti, Maurizio Grasselli +2

The nonlocal Cahn-Hilliard equation provides a natural extension of the classical model for phase separation by incorporating long-range interactions through a singular convolution…

Asymptotic stabilization of weak solutions to phase-field equations with non-degenerate mobility and singular potential

Maurizio Grasselli, Andrea Poiatti

A common paradigm in phase-field models with singular potentials is that global-in-time weak solutions converge to a single equilibrium only after undergoing asymptotic regularizat…

The Cahn--Hilliard--Darcy--Forchheimer system with surfactant: Existence and long-time behavior of global weak solutions

Maurizio Grasselli, Bohan Ouyang, Andrea Poiatti +1

We consider a diffuse-interface model for two-phase incompressible viscous flows with a soluble surfactant in a bounded porous medium. This hydrodynamic system consists of a Darcy-…

Long-time dynamics of a bulk-surface convective Cahn--Hilliard system: Pullback attractors and convergence to equilibrium

Patrik Knopf, Andrea Poiatti, Jonas Stange +1

We study the long-time dynamics of a bulk-surface convective Cahn--Hilliard system describing phase separation processes with bulk-surface interaction. The presence of convection t…

Well-posedness and sharp interface limit of a non-isothermal Navier--Stokes/Allen--Cahn model

Helmut Abels, Alice Marveggio, Andrea Poiatti

We propose a thermodynamically consistent phase-field model for the flow of a mixture of two different viscous incompressible fluids of equal density in a bounded domain. We prove…

Convergence to equilibrium of weak solutions to the Cahn--Hilliard equation with non-degenerate mobility and singular potential

Maurizio Grasselli, Andrea Poiatti

We consider the classical initial and boundary value problem for the Cahn--Hilliard equation with non-degenerate mobility and singular (e.g., logarithmic) potential. We prove that…

Varifold solutions to Volume-Preserving Mean Curvature Flow: existence and weak-strong uniqueness

Andrea Poiatti

In this contribution we introduce a novel weak solution concept for two-phase volume-preserving mean curvature flow, having both properties of unconditional global-in-time existenc…

Weak Solutions to a Sharp Interface Model for a Two-Phase Flow of Incompressible Viscous Fluids with Different Densities

Helmut Abels, Andrea Poiatti

In this paper we consider the flow of two incompressible, viscous and immiscible fluids in a bounded domain, with different densities and viscosities. This model consists of a coup…

Weak solutions and sharp interface limit of the anisotropic Cahn-Hilliard equation with disparate mobility and inhomogeneous potential

Charles Elbar, Andrea Poiatti

We study the existence of weak solutions and the corresponding sharp interface limit of an anisotropic Cahn-Hilliard equation with disparate mobility, i.e., the mobility is degener…

Long-Time behavior of the tangential surface Navier-Stokes equation

Andrea Poiatti, Ulisse Stefanelli

We investigate the initial-value problem for the incompressible tangential Navier-Stokes equation with variable viscosity on a given two-dimensional surface without boundary. Exist…

Multi-component phase separation and small deformations of a spherical biomembrane

Diogo Caetano, Charles M. Elliott, Maurizio Grasselli +1

We focus on the derivation and analysis of a model for multi-component phase separation occurring on biological membranes, inspired by observations of lipid raft formation. The mod…

Diffuse Interface Model for Two-Phase Flows on Evolving Surfaces with Different Densities: Global Well-Posedness

Helmut Abels, Harald Garcke, Andrea Poiatti

We show existence and uniqueness of strong solutions to a Navier-Stokes/Cahn-Hilliard type system on a given two-dimensional evolving surface in the case of different densities and…

Diffuse Interface Model for Two-Phase Flows on Evolving Surfaces with Different Densities: Local Well-Posedness

Helmut Abels, Harald Garcke, Andrea Poiatti

A Cahn-Hilliard-Navier-Stokes system for two-phase flow on an evolving surface with non-matched densities is derived using methods from rational thermodynamics. For a Cahn-Hilliard…