The Sharp Interface Limit of a Navier–Stokes/Allen–Cahn System with Constant Mobility: Convergence Rates by a Relative Energy Approach
Sebastian Hensel, Yuning Liu
Source abstract
Abstract. We investigate the sharp interface limit of a diffuse interface system that couples the Allen–Cahn equation with the instationary Navier–Stokes system in a bounded domain in [Formula: see text] with [Formula: see text]. This model is used to describe a propagating front in a viscous incompressible flow with the width of the transition layer being characterized by a small parameter [Formula: see text]. We show that the solutions converge to a limit two-phase fluid system with surface tension that couples the mean curvature flow and the Navier–Stokes system. The main assumptions are that the evolution of the limit system is sufficiently regular and that the associated evolving interface does not intersect the boundary of the container. For quantitatively well-prepared initial data, we even establish an optimal convergence rate. This is the first rigorous result of this kind which is valid in all physically relevant ambient dimensions.
Evidence graph
No public relationships recorded yet.
Integrity note: This page is a factual metadata record created by deterministic ingestion. It is not a claim that the work moves a mathematical frontier or has been independently verified.