PreprintCC BY 4.0HAL
Asymptotics of Laplace and Stokes solutions in the gap between a sharp tip and a smooth boundary
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.
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BibTeX
@misc{roblet2026asymptotics,
title = {{Asymptotics of Laplace and Stokes solutions in the gap between a sharp tip and a smooth boundary}},
author = {Nicolas Roblet},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17377},
eprint = {2609.17377},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05747044v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Asymptotics of Laplace and Stokes solutions in the gap between a sharp tip and a smooth boundary
AU - Nicolas Roblet
PY - 2026
DA - 2026/09/11
PB - HAL
DO - 10.48550/arxiv.2609.17377
UR - https://hal.science/hal-05747044v1
AB - 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.
ER -