# Vanishing viscosity limit of navier-stokes equations in gevrey class

## TL;DR

This paper investigates the inviscid limit of Navier-Stokes solutions in Gevrey class, demonstrating viscosity-independent lifespan and convergence to Euler solutions with a specified rate as viscosity approaches zero.

## Contribution

It establishes the convergence of Navier-Stokes solutions to Euler solutions in Gevrey class and provides the convergence rate, with lifespan independent of viscosity.

## Key findings

- Solutions' lifespan is independent of viscosity.
- Navier-Stokes solutions converge to Euler solutions in Gevrey class.
- Convergence rate in Gevrey class is quantified.

## Abstract

In this paper we consider the inviscid limit for the periodic solutions to Navier-Stokes equation in the framework of Gevrey class. It is shown that the lifespan for the solutions to Navier-Stokes equation is independent of viscosity, and that the solutions of the Navier-Stokes equation converge to that of Euler equation in Gevrey class as the viscosity tends to zero. Moreover the convergence rate in Gevrey class is presented.