# The inviscid limit of Navier-Stokes with critical Navier-slip boundary conditions for analytic data

## TL;DR

This paper proves the short-time inviscid limit of incompressible Navier-Stokes equations with critical Navier-slip boundary conditions for analytic data on a half-space, extending previous work to new boundary conditions with detailed kernel analysis.

## Contribution

It introduces a novel pointwise Green kernel bound for the Stokes problem with nonlocal boundary conditions and analyzes boundary layer behavior for vorticity.

## Key findings

- Established inviscid limit for analytic data
- Derived precise Green kernel bounds
- Propagated boundary layer behavior

## Abstract

In this paper, we establish the short time inviscid limit of the incompressible Navier-Stokes equations with critical Navier-slip boundary conditions for analytic data on half-space, a boundary condition that is physically derived from the hydrodynamic limit of the Boltzmann equations with the Maxwell boundary conditions. The analysis is built upon the recent framework developed by T. T. Nguyen and T. T. Nguyen (Arch. Ration. Mech. Anal., 230(3):1103-1129, 2018.) in the case of the classical no-slip boundary conditions. The novelty in this paper is to derive the precise pointwise bound on the Green kernel for the Stokes problem with a nonlocal boundary condition and to propagate the boundary layer behavior for vorticity.