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arXiv · 2511.04368

Strong Solutions and Applications to the Inviscid Limit for 2D Navier-Stokes with Navier Slip

Josef Demmel·Emil Wiedemann
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Abstract

We analyze the two-dimensional incompressible Navier-Stokes equations on a smooth, bounded, simply connected domain with Navier boundary conditions with friction coefficient $α\in C^2$. For initial vorticity in $L^2$, we show that the unique weak solution for velocity is, in fact, strong and satisfies the Navier slip conditions for any positive time. The key idea is to consider a shifted vorticity, which vanishes on the boundary, and to study the Laplacian subject to Navier boundary conditions. We prove that this boundary-value problem is elliptic in the sense of Agmon-Douglis-Nirenberg. As an application of this scheme, we establish uniform-in-time strong convergence of the vorticity in the vanishing viscosity limit for initial vorticity in $L^p$ with $p>2$. We utilize a purely interior framework from Seis, Wiedemann, and Woźnicki, originally derived for no-slip, and upgrade local to global convergence. Moreover, we show that the total bulk viscous enstrophy dissipation vanishes.

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Josef Demmel, Emil Wiedemann. 2026-09-03. Strong Solutions and Applications to the Inviscid Limit for 2D Navier-Stokes with Navier Slip. https://arxiv.org/abs/2511.04368

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