Asymptotics of Laplace and Stokes solutions in the gap between a sharp tip and a smooth boundary
Year: 2026
Type: preprint
Abstract: We derive an explicit description of the asymptotic singular behavior of 2D Laplace and Stokes solutions as the distance between a Lipschitz sharp tip and a smooth boundary vanishes. While classical lubrication theory for smoother boundaries relies on the anisotropy of the gap to perform dimensional reduction, the isotropic scaling imposed by a corner singularity requires a different approach. We introduce a stability-based method that allows us to construct the leading-order asymptotics of these solutions in the gap. As an application, we determine the asymptotic behavior of the Stokes resistance matrix and the pressure field.
Source: arXiv (Cornell University)
Author: Roblet, Nicolas
Institution: Institut Montpelliérain Alexander Grothendieck
Language: English
Subfield: Mechanical Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Funder: Agence Nationale de la Recherche
OpenAlex ID: W7213425825