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Applied Mathematics and Mechanics (English Edition) ›› 2012, Vol. 33 ›› Issue (8): 1079-1092.doi: https://doi.org/10.1007/s10483-012-1606-9

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Equations of Langmuir turbulence and Zakharov equations: smoothness and approximation

游淑军1,2, 郭柏灵3, 宁效琦2   

  1. 1. School of Mathematical Science and Computing Technology, Central South University, Changsha 410083, P. R. China;
    2. Department of Mathematics, Huaihua University, Huaihua 418008, Hunan Province, P. R. China;
    3. Institute of Applied Physics and Computational Mathematics, Beijing 100088, P. R. China
  • 收稿日期:2011-06-24 修回日期:2012-03-30 出版日期:2012-08-10 发布日期:2012-08-10
  • 通讯作者: Shu-jun YOU, E-mail: ysj980@yahoo.com.cn E-mail:ysj980@yahoo.com.cn
  • 基金资助:

    Project supported by the Scientific Research Fund of Hunan Provincial Education Department of China (No. 10C1056)

Equations of Langmuir turbulence and Zakharov equations: smoothness and approximation

Shu-jun YOU1,2, Bo-ling GUO3, Xiao-qi NING 2   

  1. 1. School of Mathematical Science and Computing Technology, Central South University, Changsha 410083, P. R. China;
    2. Department of Mathematics, Huaihua University, Huaihua 418008, Hunan Province, P. R. China;
    3. Institute of Applied Physics and Computational Mathematics, Beijing 100088, P. R. China
  • Received:2011-06-24 Revised:2012-03-30 Online:2012-08-10 Published:2012-08-10
  • Supported by:

    Project supported by the Scientific Research Fund of Hunan Provincial Education Department of China (No. 10C1056)

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摘要： A family of systems parameterized by H > 0, which describes the Langmuir turbulence, is considered. The asymptotic behavior of the solutions (EH, nH) when H goes to zero is studied. The results of convergence of (EH, nH) to the couple (E, n) which is the solution to the Zakharov equations are stated.

关键词: two-dimensional quasicrystal, mode-Ⅱ Griffith crack, stress function, stress intensity factor, strain energy release rate

Abstract: A family of systems parameterized by H > 0, which describes the Langmuir turbulence, is considered. The asymptotic behavior of the solutions (EH, nH) when H goes to zero is studied. The results of convergence of (EH, nH) to the couple (E, n) which is the solution to the Zakharov equations are stated.

Key words: two-dimensional quasicrystal, mode-Ⅱ Griffith crack, stress function, stress intensity factor, strain energy release rate

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