# Real variable methods in harmonic analysis and Navier-Stokes equations

## TL;DR

This paper discusses how real variable harmonic analysis methods, developed by E.M. Stein, are powerful tools for studying nonlinear PDEs, with a focus on the modern theory of Navier-Stokes equations.

## Contribution

It illustrates the application of real variable harmonic analysis techniques to advance understanding of Navier-Stokes equations.

## Key findings

- Demonstrates the effectiveness of harmonic analysis in PDE research
- Provides insights into the modern theory of Navier-Stokes equations
- Highlights the role of real variable methods in nonlinear PDE analysis

## Abstract

Real variable methods in harmonic analysis were developed throughout the works of E.M. Stein. They turn out to be a powerful tool for the study of non-linear PDEs. We illustrate this point by discussing various points of the modern theory of Navier-Stokes equations.