Application of harmonic analysis techniques to regularity problems of dissipative equations

TL;DR

This paper reviews recent progress in understanding the regularity of fluid equations, highlighting how harmonic analysis techniques provide sharper results than traditional energy methods.

Contribution

It demonstrates the effectiveness of harmonic analysis in improving regularity results for dissipative fluid equations over classical approaches.

Findings

Harmonic analysis yields sharper regularity conditions.

Recent advances improve understanding of fluid equation regularity.

Comparison shows advantages over classical energy methods.

Abstract

We discuss recent advances in the regularity problem of a variety of fluid equations and systems. The purpose is to illustrate the advantage of harmonic analysis techniques in obtaining sharper conditional regularity results when compared to classical energy methods.