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.
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