LOCAL REGULARITY NEAR BOUNDARY FOR THE STOKES AND NAVIER-STOKES EQUATIONS

被引：3

作者：

Chang, Tongkeun ^{[1
]}

Kang, Kyungkeun ^{[1
]}

机构：

[1] Yonsei Univ, Dept Math, Seoul 03722, South Korea

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2023年 / 55卷 / 05期

基金：

新加坡国家研究基金会;

关键词：

Stokes equations; Navier-Stokes equations; local regularity near boundary; SYSTEM; SPACES;

D O I：

10.1137/22M150397X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We are concerned with local regularity of the solutions for the Stokes and Navier-Stokes equations near boundary. First, we construct a bounded solution, but its normal derivatives are singular in any L-p with 1 < p locally near boundary. On the other hand, we present criteria of solutions of the Stokes equations near boundary to imply that the gradients of solutions are bounded (in fact, even further Holder continuous). Finally, we provide examples of solutions whose local regularity near boundary is optimal.

引用

页码：5051 / 5085

页数：35

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