Boussinesq方程解的部分正则性

Partial Regularity Problem of the Boussinesq Equations

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.

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.