中文摘要：

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.

英文摘要：

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.