The Minkowski dimension of boundary singular points in the Navier-Stokes equations

被引：2
|
作者：
Choe, Hi Jun [1 ]
Yang, Minsuk [1 ]
机构：
[1] Yonsei Univ, Dept Math, 50 Yonseiro, Seoul, South Korea
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2019年 / 267卷 / 08期
基金：
新加坡国家研究基金会;
关键词：
Navier-Stokes equations; Boundary suitable weak solutions; Minkowski dimension; Boundary singular points; SUITABLE WEAK SOLUTIONS; FRACTAL DIMENSION; SET; REGULARITY;
D O I：
10.1016/j.jde.2019.05.014
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study the partial regularity problem of the three-dimensional incompressible Navier-Stokes equations. We present a new boundary regularity criterion for boundary suitable weak solutions. As an application, a bound for the parabolic Minkowski dimension of possible singular points on the boundary is obtained. (C) 2019 Elsevier Inc. All rights reserved.
引用
收藏
页码：4705 / 4718
页数：14
相关论文
共 50 条
  • [1] The Minkowski dimension of interior singular points in the incompressible Navier-Stokes equations
    Koh, Youngwoo
    Yang, Minsuk
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2016, 261 (06) : 3137 - 3148
  • [2] Improved bounds for box dimensions of potential singular points to the Navier-Stokes equations
    Wang, Yanqing
    Yang, Minsuk
    NONLINEARITY, 2019, 32 (12) : 4817 - 4833
  • [3] Fractal dimension of potential singular points set in the Navier-Stokes equations under supercritical regularity
    Wang, Yanqing
    Wu, Gang
    PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2024, 154 (03) : 727 - 745
  • [4] On the Dimension of the Singular Set of Solutions to the Navier-Stokes Equations
    Robinson, James C.
    Sadowski, Witold
    COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2012, 309 (02) : 497 - 506
  • [5] A REMARK ON THE BOX-COUNTING DIMENSION OF THE SINGULAR SET FOR THE NAVIER-STOKES EQUATIONS
    Sadowski, Witold
    COMMUNICATIONS IN MATHEMATICAL SCIENCES, 2013, 11 (02) : 597 - 602
  • [6] On possible singular solutions to the Navier-Stokes equations
    Málek, J
    Necas, J
    Pokorny, M
    Schonbek, ME
    MATHEMATISCHE NACHRICHTEN, 1999, 199 : 97 - 114
  • [7] Stokes and Navier-Stokes equations with Navier boundary conditions
    Acevedo Tapia, P.
    Amrouche, C.
    Conca, C.
    Ghosh, A.
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2021, 285 : 258 - 320
  • [8] On the interior regularity criteria and the number of singular points to the Navier-Stokes equations
    Wang, Wendong
    Zhang, Zhifei
    JOURNAL D ANALYSE MATHEMATIQUE, 2014, 123 : 139 - 170
  • [9] Navier-Stokes equations with Navier boundary condition
    Amrouche, Cherif
    Rejaiba, Ahmed
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2016, 39 (17) : 5091 - 5112
  • [10] Some results on the Navier-Stokes equations with Navier boundary conditions
    Berselli, Luigi C.
    RIVISTA DI MATEMATICA DELLA UNIVERSITA DI PARMA, 2010, 1 (01): : 1 - 75
12345