7 papers
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…
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-…
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…
Global Weak Solutions of a Thermodynamically Consistent Diffuse Interface Model for Nonhomogeneous Incompressible Two-phase Flows with a Soluble Surfactant
Bohan Ouyang, Maurizio Grasselli, Hao Wu
We study a thermodynamically consistent diffuse interface model that describes the motion of a two-phase flow of two viscous incompressible Newtonian fluids with unmatched densitie…