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
  • [31] Global regularity to the 3D incompressible MHD equations
    Zhang, Peixin
    Yu, Haibo
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2015, 432 (02) : 613 - 631
  • [32] A Regularity Criterion for the 3D Generalized MHD Equations
    Jishan Fan
    Ahmed Alsaedi
    Tasawar Hayat
    Gen Nakamura
    Yong Zhou
    Mathematical Physics, Analysis and Geometry, 2014, 17 : 333 - 340
  • [33] Regularity for 3D MHD equations in Lorentz space
    Liu, Xiangao
    Liu, Yueli
    EUROPEAN PHYSICAL JOURNAL PLUS, 2022, 137 (02):
  • [34] Two regularity criteria for the 3D MHD equations
    Cao, Chongsheng
    Wu, Jiahong
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2010, 248 (09) : 2263 - 2274
  • [35] A Regularity Criterion for the 3D Generalized MHD Equations
    Fan, Jishan
    Alsaedi, Ahmed
    Hayat, Tasawar
    Nakamura, Gen
    Zhou, Yong
    MATHEMATICAL PHYSICS ANALYSIS AND GEOMETRY, 2014, 17 (3-4) : 333 - 340
  • [36] Regularity for 3D MHD equations in Lorentz space
    Xiangao Liu
    Yueli Liu
    The European Physical Journal Plus, 137
  • [37] 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
  • [38] 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):
  • [39] 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
  • [40] On the interior regularity of suitable weak solutions to the Navier-Stokes equations
    Chae, Dongho
    Kang, Kyungkeun
    Lee, Jihoon
    COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2007, 32 (7-9) : 1189 - 1207