一类Boussinesq方程组消失扩散极限的边界层

吉林大学学报(理学版)

一类Boussinesq方程组消失扩散极限的边界层

李华鹏¹, 朱秀丽¹, 徐中海¹, 袁洪君²

1. 东北电力大学理学院, 吉林吉林 132012； 2. 吉林大学数学学院, 长春 130012)

收稿日期:2015-07-07 出版日期:2015-09-26 发布日期:2015-09-29
通讯作者: 李华鹏 E-mail:huapeng.li@163.com

Boundary Layer of Vanishing Diffusivity Limitfor a Class of Boussinesq Equations

LI Huapeng¹, ZHU Xiuli¹, XU Zhonghai¹, YUAN Hongjun²

1. College of Science, Northeast Dianli University, Jilin 132012, Jilin Province, China;2. College of Mathematics, Jilin University, Changchun 130012, China

Received:2015-07-07 Online:2015-09-26 Published:2015-09-29
Contact: LI Huapeng E-mail:huapeng.li@163.com

摘要/Abstract

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(εβ)(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.

关键词: 边界层, 边界层厚度, 收敛率, 消失扩散极限

Abstract:

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 parameter ε→0, giving that the boundary layer thickness is of the order O(εβ) with 0<β<2/3. Compared with the existing methods, the present method presented more thinner BLthickness. In addition, the convergence rate was also improved.

Key words: boundary layer, BL-thickness, convergence rates, vanishing diffusivity limit

中图分类号:

O175.2

李华鹏, 朱秀丽, 徐中海, 袁洪君. 一类Boussinesq方程组消失扩散极限的边界层[J]. 吉林大学学报(理学版), 2015, 53(05): 930-933.

LI Huapeng, ZHU Xiuli, XU Zhonghai, YUAN Hongjun. Boundary Layer of Vanishing Diffusivity Limitfor a Class of Boussinesq Equations[J]. Journal of Jilin University Science Edition, 2015, 53(05): 930-933.

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