On the interior regularity conditions of a suitable weak solution to 3D MHD equations

被引:0
|
作者
Kim, Jae-Myoung
机构
[1] Univ Malaya, Fac Dent, Kuala Lumpur 50603, Malaysia
[2] Univ Malaya, Fac Dent, Dept Restorat Dent, Prosthodont MRACDS, Kuala Lumpur, Malaysia
[3] Univ Malaya, Fac Dent, Dept Restorat Dent, Kuala Lumpur, Malaysia
[4] Natl Univ Hlth Syst, Div Dent, Singapore, Singapore
[5] Natl Univ Hlth Syst, Ng Teng Fong Gen Hosp, Singapore, Singapore
关键词
Suitable weak solution; Local regularity condition; 3D MHD equations; SELF-ETCH ADHESIVE; POTASSIUM-IODIDE; POLYALKENOATE CEMENTS; ENAMEL;
D O I
10.2341/23-161-L
中图分类号
R78 [口腔科学];
学科分类号
1003 ;
摘要
We study the local interior regularity condition of a suitable weak solution to MHD equations. We prove that if a vorticity, w belong to Lx,tp,q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_{x,t}<^>{p,q}$$\end{document} in a neighborhood of an interior point with 3p+2q <= 2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{3}{p} + \frac{2}{q} \le 2$$\end{document} and 32<p T5, T3; LC - T5, T4, T3 > T2. SC generally exhibited adhesive failures, while LC presented both adhesive and mixed failures. Conclusion: The preferred method for preparing SDF-treated carious dentin before restoration application is PAA for SC and PPA plus RMGIC adhesive for LC HVGICs.
引用
收藏
页码:714 / 724
页数:11
相关论文
共 50 条
  • [41] Regularity criteria for 3D Hall-MHD equations
    Jia, Xuanji
    Zhou, Yong
    ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2022, 73 (06):
  • [42] Regularity criteria for the 3D MHD equations in term of velocity
    Bie, Qunyi
    Wang, Qiru
    Yao, Zheng-an
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2015, 38 (12) : 2506 - 2516
  • [43] Remark on an improved regularity criterion for the 3D MHD equations
    Xu, Xiaojing
    Ye, Zhuan
    Zhang, Zujin
    APPLIED MATHEMATICS LETTERS, 2015, 42 : 41 - 46
  • [44] Regularity criteria for the 3D MHD equations in terms of the pressure
    Zhou, Yong
    INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, 2006, 41 (10) : 1174 - 1180
  • [45] Global weighted regularity for the 3D axisymmetric MHD equations
    Guo, Zhengguang
    Wang, Yufei
    Li, Yeping
    ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2022, 73 (04):
  • [46] ON THE GEVREY REGULARITY OF SOLUTIONS TO THE 3D IDEAL MHD EQUATIONS
    Cheng, Feng
    Xu, Chao-Jiang
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2019, 39 (11) : 6485 - 6506
  • [47] Global weighted regularity for the 3D axisymmetric MHD equations
    Zhengguang Guo
    Yufei Wang
    Yeping Li
    Zeitschrift für angewandte Mathematik und Physik, 2022, 73
  • [48] Regularity for 3D inhomogeneous incompressible MHD equations with vacuum
    Kim, Jae-Myoung
    JOURNAL OF MATHEMATICAL PHYSICS, 2022, 63 (11)
  • [49] Some new regularity criteria for the 3D MHD equations
    Ni, Lidiao
    Guo, Zhengguang
    Zhou, Yong
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 396 (01) : 108 - 118
  • [50] On regularity criterion to the 3D axisymmetric incompressible MHD equations
    Liu, Jitao
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2016, 39 (15) : 4535 - 4544