# On convergence criteria for incompressible Navier-Stokes equations with Navier boundary conditions and physical slip rates

## TL;DR

This paper establishes convergence criteria for weak solutions of 2D incompressible Navier-Stokes equations with Navier slip boundary conditions to Euler solutions, highlighting the critical role of slip rate dependence on Reynolds number.

## Contribution

It provides new convergence criteria considering slip rates depending on Reynolds number, especially emphasizing the potential criticality of power 1 for L^2 convergence.

## Key findings

- Convergence of weak solutions to Euler solutions under Navier boundary conditions.
- Identification of the slip rate power as a critical factor for convergence.
- Analysis suggesting power 1 as a potential threshold for L^2 convergence.

## Abstract

We prove some criteria for the convergence of weak solutions of the 2D incompressible Navier-Stokes equations with Navier slip boundary conditions to a strong solution of incompressible Euler. The slip rate depends on a power of the Reynolds number, and it is increasingly apparent that the power 1 may be critical for L^2 convergence, as hinted at in [hal-01093331].