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arXiv · 2507.02775

On the two-dimensional Navier-Stokes equations with horizontal viscosity

Chongsheng Cao·Yanqiu Guo
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Abstract

This paper is concerned with a 2D channel flow that is periodic horizontally but bounded above and below by hard walls. We assume the presence of horizontal viscosity only. We study the well-posedness, large-time behavior, and stability of solutions. For global well-posedness, we aim to assume less differentiability on initial velocity $(u_0, v_0)$: in particular, we assume $u_0,v_0\in L^2(\Omega)$ and $\partial_y u_0 \in L^2(\Omega)$.

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Chongsheng Cao, Yanqiu Guo. 2025-07-03. On the two-dimensional Navier-Stokes equations with horizontal viscosity. https://arxiv.org/abs/2507.02775

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