4 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…
The stochastic nonlocal Cahn-Hilliard equation with regular potential and multiplicative noise
Andrea Di Primio, Christoph Hurm
In this work, we deal with the stochastic counterpart of the nonlocal Cahn-Hilliard equation with regular potential in a smooth bounded one-, two- or three-dimensional domain. The…
Nonlocal-to-local -convergence of convolution operators with singular, anisotropic kernels
Helmut Abels, Christoph Hurm, Patrik Knopf
We study nonlocal convolution-type operators with singular, possibly anisotropic kernels. Our main objective is to establish and quantify their nonlocal-to-local convergence to a l…
Convergence of the Nonlocal Allen-Cahn Equation to Mean Curvature Flow
Helmut Abels, Christoph Hurm, Maximilian Moser
We prove convergence of the nonlocal Allen-Cahn equation to mean curvature flow in the sharp interface limit, in the situation when the parameter corresponding to the kernel goes t…