4 citations · 4 across the 8 of their papers we have counts for
9 papers
Global Quasi-strong Solutions to the Voigt Regularization of a Diffuse Interface Model for Incompressible Two-phase Flows with Bulk-surface Interaction
Patrik Knopf, Maoyin Lv, Hao Wu
We analyze a thermodynamically consistent diffuse interface model for incompressible two-phase viscous flows with unmatched densities in a smooth bounded domain $Ω\subset\mathbb{R}…
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…
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…
Curvature-driven pattern formation in biomembranes: A gradient flow approach
Patrik Knopf, Anastasija Pešić, Dennis Trautwein
In this work, we study a phase-field model for curvature-driven pattern formation in biomembranes. The model is derived as a gradient flow of an energy functional that approximates…
A thermodynamically consistent model for bulk-surface viscous fluid mixtures: Model derivation and mathematical analysis
Patrik Knopf, Jonas Stange
We derive and analyze a new diffuse interface model for incompressible, viscous fluid mixtures with bulk-surface interaction. Our system consists of a Navier--Stokes--Cahn--Hilliar…
A Thermodynamically Consistent Free Boundary Model for Two-Phase Flows in an Evolving Domain with Bulk-Surface Interaction
Patrik Knopf, Yadong Liu
We derive a thermodynamically consistent model, which describes the time evolution of a two-phase flow in an evolving domain. The movement of the free boundary of the domain is dri…
Regularity of a bulk-surface Cahn-Hilliard model driven by Leray velocity fields
Andrea Giorgini, Patrik Knopf, Jonas Stange
We consider a convective bulk-surface Cahn--Hilliard system with dynamic boundary conditions and singular potentials. For this model, well-posedness results concerning weak and str…
Strong well-posedness and separation properties for a bulk-surface convective Cahn--Hilliard system with singular potentials
Patrik Knopf, Jonas Stange
This paper addresses the well-posedness of a general class of bulk-surface convective Cahn--Hilliard systems with singular potentials. For this model, we first prove the existence…
Nonlocal-to-local convergence rates for strong solutions to a Navier-Stokes-Cahn-Hilliard system with singular potential
Christoph Hurm, Patrik Knopf, Andrea Poiatti
The main goal of this paper is to establish the nonlocal-to-local convergence of strong solutions to a Navier--Stokes--Cahn--Hilliard model with singular potential describing immis…