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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.04368 |
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| _version_ | 1866917065422536704 |
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| author | Demmel, Josef Wiedemann, Emil |
| author_facet | Demmel, Josef Wiedemann, Emil |
| contents | We analyze the two-dimensional incompressible Navier-Stokes equations on a smooth, bounded domain with Navier boundary conditions. Starting from an initial vorticity in $L^p$ with $p>2$, we show strong convergence of the vorticity in the vanishing viscosity limit. We utilize a purely interior framework from Seis, Wiedemann, and Woźnicki, originally derived for no-slip, and upgrade local to global convergence. Under the same assumptions, we also show that the velocity is in fact a strong solution and satisfies the Navier slip conditions for any positive time. The key idea is to study the Laplacian subject to Navier boundary conditions and prove that this boundary-value problem is elliptic in the sense of Agmon-Douglis-Nirenberg. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_04368 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | 2D Navier-Stokes with Navier Slip: Strong Vorticity Convergence and Strong Solutions for Unbounded Vorticity Demmel, Josef Wiedemann, Emil Analysis of PDEs 35Q30, 35Q31, 35Q35, 75D05 We analyze the two-dimensional incompressible Navier-Stokes equations on a smooth, bounded domain with Navier boundary conditions. Starting from an initial vorticity in $L^p$ with $p>2$, we show strong convergence of the vorticity in the vanishing viscosity limit. We utilize a purely interior framework from Seis, Wiedemann, and Woźnicki, originally derived for no-slip, and upgrade local to global convergence. Under the same assumptions, we also show that the velocity is in fact a strong solution and satisfies the Navier slip conditions for any positive time. The key idea is to study the Laplacian subject to Navier boundary conditions and prove that this boundary-value problem is elliptic in the sense of Agmon-Douglis-Nirenberg. |
| title | 2D Navier-Stokes with Navier Slip: Strong Vorticity Convergence and Strong Solutions for Unbounded Vorticity |
| topic | Analysis of PDEs 35Q30, 35Q31, 35Q35, 75D05 |
| url | https://arxiv.org/abs/2511.04368 |