Gradient estimates for the non-stationary Stokes system with the Navier boundary condition

Hui Chen; Su Liang; Tai-Peng Tsai

doi:10.3934/cpaa.2023120

Article Contents

2024, Volume 23, Issue 10: 1483-1505. Doi: 10.3934/cpaa.2023120

This issue Previous Article Viscous shocks and long-time behavior of scalar conservation laws Next Article Local and global regularity for the Stokes and Navier-Stokes equations with boundary data in the half-space

Gradient estimates for the non-stationary Stokes system with the Navier boundary condition

1.
School of Science, Zhejiang University of Science and Technology, Hangzhou, 310023, P. R. China
2.
Department of Mathematics, University of British Columbia, Vancouver, BC V6T1Z2, Canada

^*Corresponding author: Tai-Peng Tsai
^*Corresponding author: Tai-Peng Tsai

Dedicated to Professor Vladimír Šverák on the occasion of his 65th birthday

Received: June 2023

Revised: July 2023

Early access: November 2023

Published: October 2024

Hui Chen was supported in part by National Natural Science Foundation of China under the grant [12101556] and China Scholarship Council. The research of both Liang and Tsai was partially supported by Natural Sciences and Engineering Research Council of Canada (NSERC) grants RGPIN-2018-04137 and RGPIN-2023-04534.

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Abstract

For the non-stationary Stokes system, it is well-known that one can improve spatial regularity in the interior, but not near the boundary if it is coupled with the no-slip boundary condition. In this note we show that, to the contrary, spatial regularity can be improved near a flat boundary if it is coupled with the Navier boundary condition, with either infinite or finite slip length. The case with finite slip length is more difficult than the case with infinite slip length.

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Mathematics Subject Classification: Primary: 35Q30, 35B65.

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