LIU Fa-gui. Life-Span of Classical Solutions for One Dimensional Hydromagnetic Flow[J]. Applied Mathematics and Mechanics, 2007, 28(4): 462-470.
Citation: LIU Fa-gui. Life-Span of Classical Solutions for One Dimensional Hydromagnetic Flow[J]. Applied Mathematics and Mechanics, 2007, 28(4): 462-470.

Life-Span of Classical Solutions for One Dimensional Hydromagnetic Flow

  • Received Date: 2005-05-27
  • Rev Recd Date: 2007-01-10
  • Publish Date: 2007-04-15
  • The Cauchy problem for one dimensional hydromagnetic dynamics with dissipative terms is concerned with. For the case of non-dissipation, it is shown that the smooth solutions will develop shocks in the finite time, if the initial amounts of entropy and themagnetic field. is smaller than that of sound waves. And for the case of dissipation, the initial amounts of entropy, dissipative effect and the-magnetic field. in each period is smaller than that of sound waves. Then the smooth solutions must blow up in the finite time. Moreover, the life-span of smooth solution is given.
  • loading
  • [1]
    Jeffery A.Magnetohydrodynamics[M].New York:Interscience,1966.
    [2]
    Cabannes H.Theoretical Magnetofluid Dynamics[M].Applied Mathematics and Mechanics 13.New York:Academic Press,1970.
    [3]
    Rammaha M A.On the formation of singularities in magnetohydrodynamics waves[J].J Math Anal Appl,1994,188(4):940-955. doi: 10.1006/jmaa.1994.1472
    [4]
    KONG De-xing.Formation of singularities in one dimensional hydromagnetic flow[J].Comm Theoret Phys,2000,37(4):385-392.
    [5]
    Shankar R,Bhardwaj D.On reactive shock in magnetogasdynamics flow[J].J Math Appl Anal,1993,129(3):335-348.
    [6]
    LIU Fa-gui.Global classical solutions for one dimensional hydromagnetic flow with dissipative terms[J].J Partial Differential Equations,2002,15(1):23-38.
    [7]
    KONG De-xing.Life-span of classical solutions to quasilinear hyperbolic systems with slow decay initial data[J].Chinese Ann of Math,Ser B,2000,21(4):413-440. doi: 10.1142/S0252959900000431
    [8]
    LI Tatsien,KONG De-xing.Blow up of periodic solutions to quasilinear hyperbolic systems[J].Nonlinear Anal,1996,26(11):1779-1789. doi: 10.1016/0362-546X(94)00366-P
    [9]
    KONG De-xing.Cauchy Problem for Quasilinear Hyperbolic Systems[M].MSJ Memoirs.Vol 6.Tokyo:The Mathematical Society of Japan,2000.
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (2983) PDF downloads(752) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return