具有Navier边界条件的非平稳Stokes系统的梯度估计

IF 1 3区数学 Q1 MATHEMATICS

Communications on Pure and Applied Analysis Pub Date : 2023-01-01 DOI:10.3934/cpaa.2023120

Hui Chen, Su Liang, Tai-Peng Tsai

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引用次数: 0

摘要

对于非平稳Stokes系统，众所周知，如果与无滑移边界条件相结合，可以在内部改善空间规则性，但在边界附近却不能。在这篇笔记中，我们表明，相反，如果与无限或有限滑移长度的Navier边界条件耦合，则在平坦边界附近的空间正则性可以得到改善。有限滑移长度的情况比无限滑移长度的情况更困难。

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

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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来源期刊

Communications on Pure and Applied Analysis 数学-数学

CiteScore

1.90

自引率

10.00%

发文量

124

审稿时长

4-8 weeks

期刊介绍： CPAA publishes original research papers of the highest quality in all the major areas of analysis and its applications, with a central theme on theoretical and numeric differential equations. Invited expository articles are also published from time to time. It is edited by a group of energetic leaders to guarantee the journal''s highest standard and closest link to the scientific communities.