Simplified a priori Estimate for the Time Periodic Burgers' Equation

TL;DR

This paper introduces a simplified a priori estimate for establishing the existence and uniqueness of time periodic solutions to the viscous Burgers' equation with irregular forcing, improving upon previous estimates in terms of simplicity.

Contribution

It provides a more straightforward a priori estimate for the Burgers' equation with irregular forcing, extending the theoretical understanding of solutions with lower regularity.

Findings

Established existence and uniqueness of solutions with irregular forcing

Developed a simpler a priori estimate compared to previous methods

Extended results to forcing terms with Sobolev regularity -1 in space

Abstract

We present here a version of the existence and uniqueness result of time periodic solutions to the viscous Burgers equation with irregular forcing terms (with Sobolev regularity -1 in space). The key result here is an a priori estimate which is simpler than the previously treated case of forcing terms with regularity -1/2 in time.