论文标题
Dorodnitzyn气态边界层限制公式的近似解决方案
Approximate solutions for Dorodnitzyn's gaseous boundary layer limit formula
论文作者
论文摘要
Oleinik's \ emph {no back-flow}条件可确保矩形域中的prandtl方程的解决方案的存在和唯一性，$ r \ r \ subset \ subset \ mathbb {r}^2 $。它还使我们能够找到dorodnitzyn固定的compre \ - 可言边界层的限制公式，并在平面$ \ mathbb {r}^2 $中的有界凸域上具有恒定的总能量。在相同的假设下，如果$ | U | \ frac {4u^2} {3} z^4 \ right]+o（z^5），\]，当一个小参数$ε$由域的最大高度给出的小参数$ε$时，该域的最大高度的最大高度均按长度除以其长度为零。在这里，$ c> 0 $，$δ$是dorodnitzyn的坐标中边界层的高度，$ u $是域上边界上边界处的\ emph {free-stream}速度，而$ t_0 $是绝对表面温度。
Oleinik's \emph{no back-flow} condition ensures the existence and uniqueness of solutions for the Prandtl equations in a rectangular domain $R\subset \mathbb{R}^2$. It also allowed us to find a limit formula for Dorodnitzyn's stationary compre\-ssible boundary layer with constant total energy on a bounded convex domain in the plane $\mathbb{R}^2$. Under the same assumption, we can give an approximate solution $u$ for the limit formula if $|u|<\!\!<\!\!<1$: \[u(z)\cong δ* c * \left[z+\frac{6}{25}\cdot \frac{1}{2i_0} \cdot \frac{4U^2}{3}z^4\right]+o(z^5),\] that corresponds to an approximate horizontal velocity component when a small parameter $ε$ given by the quotient of the maximum height of the domain divided by its length tends to zero. Here, $c>0$, $δ$ is the boundary layer's height in Dorodnitzyn's coordinates, $U$ is the \emph{free-stream} velocity at the upper boundary of the domain, and $T_0$ is the absolute surface temperature.
