# Eventual regularization of the slightly supercritical fractional Burgers equation

## TL;DR

This paper proves that solutions to a slightly supercritical fractional Burgers equation become Holder continuous over time, indicating regularization effects in such nonlinear PDEs.

## Contribution

It establishes the eventual regularization of weak solutions in a supercritical fractional Burgers equation, a novel result in the analysis of nonlinear PDEs.

## Key findings

- Weak solutions become Holder continuous over time
- Regularization occurs despite supercriticality
- Results apply to a class of fractional PDEs

## Abstract

We prove that a weak solution of a slightly supercritical fractional Burgers equation becomes Holder continuous for large time.