# Inviscid limit to the shock waves for the fractal Burgers equation

## TL;DR

This paper proves the convergence of solutions of the fractal Burgers equation to entropy shocks as viscosity vanishes, providing explicit rates of convergence in the $L^2$ norm for large initial disturbances.

## Contribution

It is the first to quantify the inviscid limit to entropy shocks for the fractal Burgers equation with large initial perturbations.

## Key findings

- Established $L^2$ convergence rates in the inviscid limit.
- Proved convergence for large initial perturbations.
- First quantitative analysis for fractal Burgers equation shocks.

## Abstract

We show the vanishing viscosity limit to entropy shocks for the fractal Burgers equation in one space dimension. More precisely, we quantify the rate of convergence of the inviscid limit in $L^2$ for large initial perturbations around the entropy shock on any bounded time interval. This is the first result on the inviscid limit to entropy shock for the fractal Burgers equation with the quantified convergence, for large initial perturbations.