Local well-posedness of the boundary layer for a pseudo-plastic fluid by energy methods

Zhonger Wu; Zhong Tan

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arXiv · 2608.05693

Local well-posedness of the boundary layer for a pseudo-plastic fluid by energy methods

Zhonger Wu·Zhong Tan

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Abstract

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 Fa\`a di Bruno formula to obtain precise control over the high-order derivatives of viscosity, which is the main contribution of this paper.

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Zhonger Wu, Zhong Tan. 2026-08-06. Local well-posedness of the boundary layer for a pseudo-plastic fluid by energy methods. https://arxiv.org/abs/2608.05693

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