English

Constrained large solutions to Leray's problem in a distorted strip with the Navier-slip boundary condition

Analysis of PDEs 2023-09-18 v2

Abstract

In this paper, we will solve the Leray's problem for the stationary Navier-Stokes system in a 2D infinite distorted strip with the Navier-slip boundary condition. The existence, uniqueness, regularity and asymptotic behavior of the solution will be investigated. Moreover, we discuss how the friction coefficient affects the well-posedness of the solution. Due to the validity of the Korn's inequality, all constants in each a priori estimate are independent of the friction coefficient. The main novelty is the total flux of the velocity can be relatively large (proportional to the {\it slip length}) when the friction coefficient of the Navier-slip boundary condition is small, which is essentially different from the 3D case.

Keywords

Cite

@article{arxiv.2210.12615,
  title  = {Constrained large solutions to Leray's problem in a distorted strip with the Navier-slip boundary condition},
  author = {Zijin Li and Xinghong Pan and Jiaqi Yang},
  journal= {arXiv preprint arXiv:2210.12615},
  year   = {2023}
}

Comments

45 pages. arXiv admin note: text overlap with arXiv:2204.10578. A remark is added to state the independent accomplishment of solving the 2D Leray's problem with the Navier-slip boundary condition by our group and Professor Chunjing Xie's group