AI 中文总结
本文在Oleinik单调性假设下，运用能量方法，结合Masmoudi与Wong的抵消机制及Faà di Bruno公式，解决拟塑性流体边界层的导数损失与黏性难点，实现其局部适定性。
AI 中文摘要
我们在Oleinik单调性假设下，通过能量方法研究拟塑性流体边界层的适定性，需解决两大难点：导数损失和黏性带来的困难。针对前者，我们借鉴了Masmoudi和Wong[CPAM,2015]提出的抵消机制；针对后者，我们结合单调性假设与Faà di Bruno公式，实现对黏性高阶导数的精确控制，这是本文的主要贡献。
英文摘要
We study the well-posedness of the boundary layer for a pseudo-plastic fluid by energy methods under Oleinik's monotonicity assumption. We need to address two main difficulties: derivative loss and the difficulty caused by viscosity. For the first difficulty, we borrow the cancellation mechanism proposed by Masmoudi and Wong [CPAM, 2015]. For the second difficulty, we combine the monotonicity assumption and Faà di Bruno formula to obtain precise control over the high-order derivatives of viscosity, which is the main contribution of this paper.
