一维磁流体力学方程组经典解的生命区间

基金项目: 国家自然科学基金资助项目(10571024);河南省自然科学基金资助项目(200510078005);河南省教育厅科学基金资助项目(200511051700)

Life-Span of Classical Solutions for One Dimensional Hydromagnetic Flow

North China Institute of Water Conservancy and Hydroelectric Power, Zhengzhou 450011, P. R. China

摘要: 考虑具耗散项的一维磁流体力学方程组Cauchy问题．对于非耗散情形证明了如果初始能量和磁场强度弱于声波的能量，则Cauchy问题的光滑解在有限时间内破裂；对于耗散情形，如果初始能量、磁场强度和耗散强度弱于声波的能量，则Cauchy问题的光滑解在有限时间内破裂，而且给出了生命区间估计．
- 磁流体力学方程组 /
- Cauchy问题 /
- 经典解 /
- 耗散机制 /
- 生命区间
Abstract: 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.
- hydromagnetic flow /
- Cauchy problem /
- classical solution /
- life-span /

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