On the two-dimensional Navier-Stokes equations with horizontal viscosity
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916824514297856 |
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| author | Cao, Chongsheng Guo, Yanqiu |
| author_facet | Cao, Chongsheng Guo, Yanqiu |
| contents | 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 $u_0,v_0\in L^2(Ω)$ and $\partial_y u_0 \in L^2(Ω)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_02775 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the two-dimensional Navier-Stokes equations with horizontal viscosity Cao, Chongsheng Guo, Yanqiu Analysis of PDEs 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 $u_0,v_0\in L^2(Ω)$ and $\partial_y u_0 \in L^2(Ω)$. |
| title | On the two-dimensional Navier-Stokes equations with horizontal viscosity |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2507.02775 |