16 papers · 1 filter
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…
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…