English

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

R2 v1 2026-06-28T12:50:32.281Z