Abstract In this paper, we give a new direct proof by energy method for the local well-posedness of the boundary layer equations for two-dimensional compressible isentropic flow with no-slip boundary condition. It requires less compatibility conditions than the previous result using Nash-Moser-Hormander iteration scheme and linear energy estimates. It shows that maximum principle works for boundary layer equations so that the weighted L ∞ estimates on the lower order terms can be obtained.

中文翻译：

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二维可压缩流边界层方程解的局部适定性

摘要 在本文中，我们对二维可压缩等熵无滑移边界条件下边界层方程的局部适定性给出了一种新的能量法直接证明。与使用 Nash-Moser-Hormander 迭代方案和线性能量估计的先前结果相比，它需要更少的兼容性条件。它表明最大值原理适用于边界层方程，因此可以获得对低阶项的加权 L ∞ 估计。