A class of exact solutions for N-dimensional incompressible magnetohydrodynamic equations

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• 作者：Ping Liu
• 关键词：incompressible magnetohydrodynamic (MHD) equation ; exact solution ; symmetric matrix ; quadratic form ; curve integration ; O175.1 ; O357.1 ; 35Q35 ; 35C05 ; 76B03 ; 76M60
• 刊名：Applied Mathematics and Mechanics
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：37
• 期：2
• 页码：209-214
• 全文大小：126 KB
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  [8]Arnold, V. I. Sur la topologie des ecoulements stationnaires des fluides parfaits. Comptes Rendus Hebdomadaires Des séances De L’académie Des Sciences, 261, 17–20 (1965)
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  [11]Ye, Z. Two regularity criteria to the 2D generalized MHD equations with zero magnetic diffusivity. Journal of Mathematical Analysis and Applications, 420, 954–971 (2014)MathSciNet CrossRef
  
• 作者单位：Ping Liu (1)
  
  1. School of Management, Tianjin Normal University, Tianjin, 300387, China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Applications of Mathematics
  Mechanics
  Mathematical Modeling and IndustrialMathematics
  Chinese Library of Science
  
• 出版者：Shanghai University, in co-publication with Springer
• ISSN：1573-2754

文摘

In this paper, a sufficient and necessary condition is presented for existence of a class of exact solutions to N-dimensional incompressible magnetohydrodynamic (MHD) equations. Such solutions can be explicitly expressed by appropriate formulae. Once the required matrices are chosen, solutions to the MHD equations are directly constructed. Keywords incompressible magnetohydrodynamic (MHD) equation exact solution symmetric matrix quadratic form curve integration