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Langmuir扰动方程和Zakharov方程:光滑性与近似

游淑军 郭柏灵 宁效琦

游淑军, 郭柏灵, 宁效琦. Langmuir扰动方程和Zakharov方程:光滑性与近似[J]. 应用数学和力学, 2012, 33(8): 1013-1024. doi: 10.3879/j.issn.1000-0887.2012.08.009
引用本文: 游淑军, 郭柏灵, 宁效琦. Langmuir扰动方程和Zakharov方程:光滑性与近似[J]. 应用数学和力学, 2012, 33(8): 1013-1024. doi: 10.3879/j.issn.1000-0887.2012.08.009
YOU Shu-jun, GUO Bo-ling, NING Xiao-qi. Equations of Langmuir Turbulence and Zakharov Equations: Smoothness and Approximation[J]. Applied Mathematics and Mechanics, 2012, 33(8): 1013-1024. doi: 10.3879/j.issn.1000-0887.2012.08.009
Citation: YOU Shu-jun, GUO Bo-ling, NING Xiao-qi. Equations of Langmuir Turbulence and Zakharov Equations: Smoothness and Approximation[J]. Applied Mathematics and Mechanics, 2012, 33(8): 1013-1024. doi: 10.3879/j.issn.1000-0887.2012.08.009

Langmuir扰动方程和Zakharov方程:光滑性与近似

doi: 10.3879/j.issn.1000-0887.2012.08.009
基金项目: 湖南省教育厅科研基金资助项目(10C1056)
详细信息
    通讯作者:

    游淑军(1979—),女,湖南人,讲师,博士(联系人.E-mail:ysj980@yahoo.com.cn).

  • 中图分类号: O175.2

Equations of Langmuir Turbulence and Zakharov Equations: Smoothness and Approximation

  • 摘要: 考虑了一类带参数H,用于描述Langmuir扰动的方程.研究了当参数H趋于0时,这一类扰动方程的渐近行为.通过建立一个弱收敛结果和一个强收敛结果,得到了这类扰动方程初值问题的解(EH ,nH )收敛到Zakharov方程初值问题的解(E,n)的结论.
  • [1] Zakharov V E. Collapse of Langmuir waves[J]. Sov Phys JETP, 1972, 35: 908-914.
    [2] Pecher H. An improved local well-posedness result for the one-dimensional Zakharov system[J]. J Math Anal Appl, 2008, 342(2): 1440-1454.
    [3] Guo B, Zhang J, Pu X. On the existence and uniqueness of smooth solution for a generalized Zakharov equation[J]. J Math Anal Appl, 2010, 365(1): 238-253.
    [4] Linares F, Matheus C. Well posedness for the 1D Zakharov-Rubenchik system[J]. Advances in Differential Equations, 2009, 14(3/4): 261-288.
    [5] Masmoudi N, Nakanishi K. Energy convergence for singular limits of Zakharov type systems[J]. Invent Math, 2008, 172(3): 535-583.
    [6] Garcia L G, Haas F, de Oliveira L P L, Goedert J. Modified Zakharov equations for plasmas with a quantum correction[J]. Phys Plasmas, 2005, 12(1): 1-8.
    [7] Lions J L. Quelques Mèthodes de Résolution des Problèmes aux Limites Non Linéaires[M]. Paris: Dunod Gauthier Villard, 1969:12, 53.
    [8] Added H, Added S. Existence globale d’une solution reguliére des equations de la turbulence de Langmuir en dimension 2[J]. C R A S, Paris, 1984, 299(12): 551-554.
    [9] Added H S. Equations of Langmuir turbulence and nonlinear Schrdinger equation: smoothness and approximation[J]. J Functional Analysis, 1988, 79(1): 183-210.
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  • 被引次数: 0
出版历程
  • 收稿日期:  2011-06-24
  • 修回日期:  2012-03-30
  • 刊出日期:  2012-08-15

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