A lecture on Navier-Stokes equations

Sylvie Monniaux

A lecture on Navier-Stokes equations

History and Overview 2026-07-21 v1 Analysis of PDEs

Authors: Sylvie Monniaux

Abstract

The content of the following pages was part of a special topics lecture given at the Australian National University during the first semester of 2026. That was a very nice expericence, I really enjoyed giving this 12 weeks (2 hours a week) lecture. It is meant to be self contained, starting with results on Fourier transform and Sobolev spaces. As a toy model, before treating the Navier-Stokes system, we focus on the non linear heat equation where the non linearity is polynomial. Ultimately, we prove existence and uniqueness of mild solutions of the Navier-Stokes equations in critical spaces. This script contains some exercises and the text of the mid-semester exam as well as the final exam.

Cite

@article{arxiv.2607.18841,
  title  = {A lecture on Navier-Stokes equations},
  author = {Sylvie Monniaux},
  journal= {arXiv preprint arXiv:2607.18841},
  year   = {2026}
}