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Boussinesq方程解的部分正则性
  • 期刊名称：应用数学学报，30（5），936-954，2007.
  • 时间：0
  • 分类：O175.29[理学—数学;理学—基础数学]
  • 作者机构：[1]首都师范大学数学科学学院,北京100037
  • 相关基金：国家自然科学基金（10431060）资助项目
  • 相关项目：Boltzman方程及其相关宏观模型
关键词： BOUSSINESQ方程, 弱解, 部分正则性, Boussinesq equations, weak solutions, partial regularity
中文摘要：

本文考虑Boussinesq方程一类合适弱解的部分正则性.我们先运用广义能量不等式和奇异积分理论得到一些无维量的估计;再通过合适弱解满足的等式,运用迭代技巧,推导出温度场的小性估计;最后由尺度分析（scaling arguments）得到了一类合适弱解的部分正则性.

英文摘要：

In this paper, we are concerned with the partial regularity of the suitable weak solutions to the three-dimensional incompressible Boussinesq equations. Firstly, based on the generalized energy inequality, we get estimates of some scaled nondimensional quantities. Secondly, we employ the iterative technique to obtain the smallness of some scaled quantities of temperature field. Finally, by scaling arguments we get the partial regularity for the suitable weak solutions.

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Boltzman方程及其相关宏观模型
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