Remark on local boundary regularity condition of a suitable weak solution to the 3D MHD equations

被引:0
|
作者
Kim, Jae-Myoung [1 ]
机构
[1] Yonsei Univ, Ctr Math Anal & Computat, Seoul 03722, South Korea
关键词
magnetohydrodynamics equations; suitable weak solutions; local regularity condition; NAVIER-STOKES EQUATIONS; MAGNETOHYDRODYNAMIC EQUATIONS; CRITERIA; PRESSURE; TERMS;
D O I
10.14232/ejqtde.2019.1.32
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We study a local regularity condition for a suitable weak solution of the magnetohydrodynamics equations in a half space R-+(3). More precisely, we prove that a suitable weak solution is Holder continuous near boundary provided that the quantity lim sup (r -> 0) 1/root r parallel to parallel to u parallel to(L2)((Bx,r+))parallel to(L infinity()(t-r2,t)()) is sufficiently small near the boundary. Furthermore, we briefly add some global regularity criteria of weak solutions to this system.
引用
收藏
页码:1 / 11
页数:11
相关论文
共 50 条
  • [41] Local Regularity of Suitable Weak Solutions to the Navier-Stokes Equations Near the Boundary
    Seregin, G. A.
    JOURNAL OF MATHEMATICAL FLUID MECHANICS, 2002, 4 (01) : 1 - 29
  • [42] Local regularity for suitable weak solutions of Navier-Stokes equations near the boundary
    Mikhailov A.
    Journal of Mathematical Sciences, 2010, 166 (1) : 40 - 52
  • [43] On local regularity for suitable weak solutions of the Navier-Stokes equations near the boundary
    Mikhailov A.S.
    Journal of Mathematical Sciences, 2011, 178 (3) : 282 - 291
  • [44] A double-logarithmically improved regularity criterion of weak solutions for the 3D MHD equations
    Ines Ben Omrane
    Sadek Gala
    Maria Alessandra Ragusa
    Zeitschrift für angewandte Mathematik und Physik, 2021, 72
  • [45] A double-logarithmically improved regularity criterion of weak solutions for the 3D MHD equations
    Ben Omrane, Ines
    Gala, Sadek
    Ragusa, Maria Alessandra
    ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2021, 72 (03):
  • [46] A regularity criterion for local strong solutions to the 3D Stokes-MHD equations
    Alghamdi, Ahmad Mohammad
    Gala, Sadek
    Ragusa, Maria Alessandra
    ANNALES POLONICI MATHEMATICI, 2020, 124 (03) : 247 - 255
  • [47] A regularity criterion of smooth solution for the 3D viscous Hall-MHD equations
    Alghamdi, A. M.
    Gala, S.
    Ragusa, M. A.
    AIMS MATHEMATICS, 2018, 3 (04): : 565 - 574
  • [48] Anisotropic Regularity Conditions for the Suitable Weak Solutions to the 3D Navier-Stokes Equations
    Wang, Yanqing
    Wu, Gang
    JOURNAL OF MATHEMATICAL FLUID MECHANICS, 2016, 18 (04) : 699 - 716
  • [49] Boundary regularity criteria for suitable weak solutions of the magnetohydrodynamic equations
    Kang, Kyungkeun
    Kim, Jae-Myoung
    JOURNAL OF FUNCTIONAL ANALYSIS, 2014, 266 (01) : 99 - 120
  • [50] Regularity criteria for 3D Hall-MHD equations
    Jia, Xuanji
    Zhou, Yong
    ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2022, 73 (06):