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arXiv · 2607.18841

A lecture on Navier-Stokes equations

Sylvie Monniaux
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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.

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Sylvie Monniaux. 2026-07-21. A lecture on Navier-Stokes equations. https://arxiv.org/abs/2607.18841

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