4 papers · 2 filters
Higher Order Convergence for the Sharp Interface Limit of 3D Navier--Stokes/Allen--Cahn Systems
Helmut Abels, Mingwen Fei, Yadong Liu +1
We show convergence of solutions to a Navier--Stokes/Allen--Cahn system as the interfacial thickness tends to zero for well-prepared initial data as long as the lim…
Local Well-Posedness of a Model for Stress-Driven Growth in the Presence of Nutrients
Helmut Abels, Julian Blawid, Georg Dolzmann
A model for morphoelastic growth, that is, growth influenced by elastic stress, driven by the absorption of nutrients is considered. The model features a multiplicative decompositi…
Sharp Interface Limit for a Mass-Conserving Navier-Stokes/Allen-Cahn System with Different Viscosities
Helmut Abels, Hanifah Mumtaz
We perform a rigorous examination of the sharp interface limit of a coupled Navier-Stokes and mass-conserving Allen-Cahn system in a two-dimensional, bounded, and smooth domain as…
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…