中文摘要：

利用能量估计的方法考虑一类Boussinesq方程组的初边值问题,研究当扩散系数ε→0时的边界层效应和收敛率,给出了边界层厚度的阶数O（εβ）（0〈β〈2/3）.结果表明,与现有方法相比所得到的边界层厚度更薄,并且提高了收敛率.

英文摘要：

We considered an initial-value problem for a class of Boussinesq equations using the energy estimate method.We mainly studied the boundary layer effect and the convergence rate as the thermal diffusion parameterε→0,giving that the boundary layer thickness is of the order O（ε^β）with0〈β〈2/3.Compared with the existing methods,the present method presented more thinner BL-thickness.In addition,the convergence rate was also improved.