Neumann Problems for the Stokes Equations in Convex Domains

Jun Geng; Zhongwei Shen

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arXiv · 2410.16650

Neumann Problems for the Stokes Equations in Convex Domains

Jun Geng·Zhongwei Shen

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Abstract

This paper studies the Neumann boundary value problems for the Stokes equations in a convex domain in $\mathbb{R}^d$. We obtain nontangential-maximal-function estimates in $L^p$ and $W^{1, p}$ estimates for $p$ in certain ranges depending on $d$. These ranges are larger than the known ranges for Lipschitz domains. The proof relies on a $W^{2, 2}$ estimate for the Stokes equations in convex domains.

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Jun Geng, Zhongwei Shen. 2024-10-22. Neumann Problems for the Stokes Equations in Convex Domains. https://arxiv.org/abs/2410.16650

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