一维磁流体力学方程组经典解的生命区间  

Life-Span of Classical Solutions for One Dimensional Hydromagnetic Flow

作　　者：刘法贵[1] 

机构地区：[1]华北水利水电学院数学系,郑州450011

出　　处：《应用数学和力学》2007年第4期462-470,共9页Applied Mathematics and Mechanics

基　　金：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)

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.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 the ‘ magnetic 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 maller 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.

关 键 词：磁流体力学方程组 CAUCHY问题 经典解 耗散机制 生命区间 

分 类 号：O175.27[理学—数学]