Estimates for stress concentration between two adjacent rigid inclusions in Stokes flow
Analysis of PDEs
2023-10-17 v1
Abstract
In this paper, we establish the estimates for the gradient and the second-order partial derivatives for the Stokes flow in the presence of two closely located strictly convex inclusions in dimension three. Moreover, the blow-up rate of the gradient is showed to be optimal by a pointwise upper bound and a lower bound in the narrowest region. We also show the optimal blow-up rate of Cauchy stress tensor. In dimensions greater than three, the upper bounds of the gradient are established. These results answer the questions raised in [25].
Cite
@article{arxiv.2310.09498,
title = {Estimates for stress concentration between two adjacent rigid inclusions in Stokes flow},
author = {Haigang Li and Longjuan Xu},
journal= {arXiv preprint arXiv:2310.09498},
year = {2023}
}
Comments
41 pages. arXiv admin note: substantial text overlap with arXiv:2204.00254