Global well-posedness of the critical Burgers equation in critical Besov spaces

TL;DR

This paper proves the global well-posedness of the critical Burgers equation in critical Besov spaces using advanced analytical techniques, extending understanding of nonlinear PDE behavior in critical function spaces.

Contribution

It establishes the global well-posedness of the critical Burgers equation in critical Besov spaces, employing the modulus of continuity and Fourier localization methods.

Findings

Global well-posedness in critical Besov spaces

Application of modulus of continuity method

Use of Fourier localization technique

Abstract

We make use of the method of modulus of continuity \cite{K-N-S} and Fourier localization technique \cite{A-H} to prove the global well-posedness of the critical Burgers equation $\partial_{t}u+u\partial_{x}u+\Lambda u=0$ in critical Besov spaces $\dot{B}^{\frac{1}{p}}_{p,1}(\mathbb{R})$ with $p\in[1,\infty)$, where $\Lambda=\sqrt{-\triangle}$.