# The Limit Behavior of the Second Grade Fluid

## TL;DR

This paper investigates how solutions of the second-grade fluid equations behave as viscosity and material parameters vanish, showing convergence to Euler equations under radial symmetry.

## Contribution

It demonstrates the independent vanishing limits of viscosity and material parameters leading to Euler equations in the second-grade fluid model with no-slip boundary conditions.

## Key findings

- Convergence from second-grade fluid to Euler system as parameters tend to zero.
- Validation of the limit behavior under radial symmetry.
- Analysis of the boundary conditions' impact on convergence.

## Abstract

In the paper, the limit behavior of solutions to the second-grade fluid system with no-slip boundary conditions is studied as both $\nu$ and $\alpha$ tend to zero. More precisely, it is verified that the convergence from second-grade fluid system to Euler system holds as $\nu$ and $\alpha$ tend to zero independently under the radial symmetry case.