Local Regularity Criteria in Terms of One Velocity Component for the Navier-Stokes Equations

被引：0

作者：

Kang, Kyungkeun ^{[1
]}

Nguyen, Dinh Duong ^{[1
]}

机构：

[1] Yonsei Univ, Dept Math, 50 Yonsei Ro, Seoul 03722, South Korea

来源：

JOURNAL OF MATHEMATICAL FLUID MECHANICS | 2023年 / 25卷 / 01期

关键词：

Local energy solutions; Suitable weak solutions; Navier-Stokes equations; one velocity component; Ladyzhenskaya-Prodi-Serrin regularity condition; SUITABLE WEAK SOLUTIONS; INTERIOR REGULARITY; PROOF;

D O I：

10.1007/s00021-022-00754-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is devoted to presenting new interior regularity criteria in terms of one velocity component for weak solutions to the Navier-Stokes equations in three dimensions. It is shown that the velocity is regular near a point z if its scaled (LtLxq)-L-p-norm of some quantities related to the velocity field is finite and the scaled (LtLxq)-L-p-norm of one velocity component is sufficiently small near z.

引用

页数：15

共 41 条

[1] Regularity condition of the incompressible Navier-Stokes equations in terms of one velocity component [J].

Bae, Hantaek ;

Kang, Kyungkeun .

APPLIED MATHEMATICS LETTERS, 2019, 94 :120-125

[2]

Bahouri H., 2011, GRUNDLEHREN MATH WIS, V343

[3] Global existence, regularity, and uniqueness of infinite energy solutions to the Navier-Stokes equations [J].

Bradshaw, Zachary ;

Tsai, Tai-Peng .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2020, 45 (09) :1168-1201

[4] PARTIAL REGULARITY OF SUITABLE WEAK SOLUTIONS OF THE NAVIER-STOKES EQUATIONS [J].

CAFFARELLI, L ;

KOHN, R ;

NIRENBERG, L .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1982, 35 (06) :771-831

[5] Regularity Criteria for the Three-dimensional Navier-Stokes Equations [J].

Cao, Chongsheng ;

Titi, Edriss S. .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2008, 57 (06) :2643-2661

[6] On the Serrin-Type Condition on One Velocity Component for the Navier-Stokes Equations [J].

Chae, D. ;

Wolf, J. .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2021, 240 (03) :1323-1347

[7] On the Critical One Component Regularity for 3-D Navier-Stokes System: General Case [J].

Chemin, Jean-Yves ;

Zhang, Ping ;

Zhang, Zhifei .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2017, 224 (03) :871-905

[8]

Chemin JY, 2016, ANN SCI ECOLE NORM S, V49, P131

[9] L3,∞-solutions of the Navier-Stokes equations and backward uniqueness [J].

Escauriaza, L ;

Seregin, G ;

Sverák, V .

RUSSIAN MATHEMATICAL SURVEYS, 2003, 58 (02) :211-250

[10] INITIAL VALUE-PROBLEM FOR NAVIER-STOKES EQUATIONS WITH DATA IN LP [J].

FABES, EB ;

JONES, BF ;

RIVIERE, NM .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1972, 45 (03) :222-&

← 1 2 3 4 5 →