On the dynamic slip boundary condition for Navier--Stokes-like problems

TL;DR

This paper develops a mathematical framework for Navier-Stokes-like problems incorporating dynamic slip boundary conditions, capturing rapid slip changes and associated stress phenomena often overlooked in static models.

Contribution

It introduces a generalized analysis for dynamic slip boundary conditions, extending existing models to better reflect rapid slip variations in fluid-surface interactions.

Findings

Mathematical formulation of dynamic slip boundary conditions.

Extension of function spaces for analysis.

Foundation for future numerical and experimental studies.

Abstract

The choice of the boundary conditions in mechanical problems has to reflect the interaction of the considered material with the surface, despite the assumption of the no-slip condition is preferred to avoid boundary terms in the analysis and slipping effects are usually overlooked. Besides the "static slip models", there are phenomena not accurately described by them, e.g. in the moment when the slip changes rapidly, the wall shear stress and the slip can exhibit a sudden overshoot and subsequent relaxation. When these effects become significant, the so-called dynamic slip phenomenon occurs. We develop a mathematical analysis of Navier-Stokes-like problems with dynamic slip boundary condition, which requires a proper generalisation of the Gelfand triplet and the corresponding function spaces setting.