Time-Periodic Solutions of the Burgers Equation

TL;DR

This paper studies time-periodic solutions to the viscous Burgers equation with irregular forcing, proving the Burgers operator is a diffeomorphism between suitable function spaces, which advances understanding of nonlinear PDEs with irregular inputs.

Contribution

It establishes the diffeomorphism property of the Burgers operator for irregular forcing, providing new insights into the existence and structure of time-periodic solutions.

Findings

Burgers operator is a diffeomorphism between specific function spaces.

Existence of time-periodic solutions for irregular forcing terms.

Enhanced understanding of nonlinear PDEs with irregular inputs.

Abstract

We investigate the time periodic solutions to the viscous Burgers equation $u_t -\mu u_{xx} + uu_x = f$ for irregular forcing terms. We prove that the corresponding Burgers operator is a diffeomorphism between appropriate function spaces.