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arXiv · 2210.12615

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

Zijin Li·Xinghong Pan·Jiaqi Yang
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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.

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Zijin Li, Xinghong Pan, Jiaqi Yang. 2022-10-23. Constrained large solutions to Leray's problem in a distorted strip with the Navier-slip boundary condition. https://doi.org/10.1016/j.jde.2023.08.043

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