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

Zhonger Wu; Zhong Tan

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

Analysis of PDEs 2026-08-06 v1

Authors: Zhonger Wu , Zhong Tan

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.

Keywords

boundary layer pseudo-plastic fluid energy methods well-posedness Oleinik monotonicity assumption derivative loss

Cite

@article{arxiv.2608.05693,
  title  = {Local well-posedness of the boundary layer for a pseudo-plastic fluid by energy methods},
  author = {Zhonger Wu and Zhong Tan},
  journal= {arXiv preprint arXiv:2608.05693},
  year   = {2026}
}