| 三维Boussinesq方程组大解的全局L~2稳定性 |
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| 引用本文： | 李现今,酒全森.三维Boussinesq方程组大解的全局L~2稳定性[J].数学学报,2010,53(1):171-186. |
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| 作者姓名： | 李现今 酒全森 |
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| 作者单位： | 中国科学院力学研究所;首都师范大学数学科学学院; |
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| 基金项目： | 国家自然科学基金资助项目(10871133,10771177) |
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| 摘 要： | 对三维有界及无界区域上的Boussinesq方程的全局L~2稳定性进行了讨论.在解满足适当的条件下,证明了此解为稳定的,并得出此稳定性条件的等价性条件,最后得出了二维Boussinesq方程组在三维扰动下的解的全局存在性和稳定性.
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| 关 键 词： | Boussinesq方程组 强解 稳定性 |
| 收稿时间： | 2007-12-10 |
| 修稿时间： | 2009-07-08 |
The Global L2 Stability of Large Solutions to Three Dimensional Boussinesq Equations |
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| Xian Jin LI Institute of Mechanics,Chinese Academy of Sciences,Beijing ,P.R.China School of Mathematics Sciences,Capital Normal University,Beijing ,P.R.China Quan Sen JIU School of Mathematics Sciences,P.R.China.The Global L2 Stability of Large Solutions to Three Dimensional Boussinesq Equations[J].Acta Mathematica Sinica,2010,53(1):171-186. |
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| Authors: | Xian Jin LI Institute of Mechanics Chinese Academy of Sciences Beijing PRChina School of Mathematics Sciences Capital Normal University Beijing PRChina Quan Sen JIU School of Mathematics Sciences PRChina |
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| Institution: | 1. Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, P. R. China;
2. School of Mathematics Sciences, Capital Normal University, Beijing 100048, P. R. China |
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| Abstract: | In this paper,we mainly study the global L~2 stability for large solutions to the Boussinesq equations in three-dimensional bounded or unbounded domains.Under suitable conditions of the large solutions,it is shown that the large solutions are stable. And we obtain the equivalent condition of this main stability condition.Moreover, the global existence and the stability of two-dimensional Boussinesq equations under three-dimensional perturbations are also established. |
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| Keywords: | Boussinesq equations strong solutions stability |
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