2D Navier-Stokes with Navier Slip: Strong Vorticity Convergence and Strong Solutions for Unbounded Vorticity

2025/11/06 by Demmel, Josef, Emil Wiedemann, Wiedemann, Emil
Engineering · Mathematics · #35Q30 #35Q31 #35Q35 #75D05 #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2511.04368

openalex publication_date 2025/11/06 · openalex created_date 2025/11/08 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Strong Convergence of Vorticities in the 2D Viscosity Limit on a Bounded Domain
• The inviscid limit for the 2d Navier-Stokes equations in bounded domains
• Inviscid limit of vorticity distributions in Yudovich class
• The Inviscid Limit and Boundary Layers for Navier-Stokes Flows
• A note on Aubin-Lions-Dubinskii lemmas

Related

• Strong Convergence of Vorticities in the 2D Viscosity Limit on a Bounded Domain
• On convergence criteria for incompressible Navier-Stokes equations with Navier boundary conditions and physical slip rates
• The vanishing viscosity limit for 2D Navier-Stokes in a rough domain
• On the inviscid limit for 2D incompressible flow with Navier friction condition
• The Navier-Stokes Equations with the Kinematic and Vorticity Boundary Conditions on Non-Flat Boundaries