三维Boussinesq 方程组大解的全局L2

李现今, 酒全森

数学学报 ›› 2010, Vol. 53 ›› Issue (1) : 171-186.

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数学学报 ›› 2010, Vol. 53 ›› Issue (1) : 171-186. DOI: 10.12386/A2010sxxb0022
论文

三维Boussinesq 方程组大解的全局L2

    李现今1,2, 酒全森2
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The Global L2 Stability of Large Solutions to Three Dimensional Boussinesq Equations

    Xian Jin LI1,2, Quan Sen JIU2
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摘要

对三维有界及无界区域上的Boussinesq方程的全局L2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.

 

Abstract

In this paper, we mainly study the global L2 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.

 

关键词

Boussinesq方程组 / 强解 / 稳定性

Key words

Boussinesq equations / strong solutions / stability

引用本文

导出引用
李现今, 酒全森. 三维Boussinesq 方程组大解的全局L2. 数学学报, 2010, 53(1): 171-186 https://doi.org/10.12386/A2010sxxb0022
Xian Jin LI, Quan Sen JIU. The Global L2 Stability of Large Solutions to Three Dimensional Boussinesq Equations. Acta Mathematica Sinica, Chinese Series, 2010, 53(1): 171-186 https://doi.org/10.12386/A2010sxxb0022

参考文献


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基金

国家自然科学基金资助项目(10871133,10771177)

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