Navier-Stokes Equations - Numberphile
Why Hacker News recommends it
HN commenters recommend it as an accessible introduction to Navier-Stokes for non-mathematicians, often when fluid dynamics or turbulence comes up.
Recommended by 3 people across 3 different months, 2019 to 2026.
What it is
Oxford mathematician Tom Crawford explains the Navier-Stokes equations for fluid flow and why proving that smooth solutions always exist is a $1m Millennium Prize problem. It is part 1 of a Numberphile series, with animations and a Navier-Stokes tattoo.
What people said
Recommends farisjarrah · 2019-12 · Hacker News · on “What Makes the Hardest Equations in Physics So Difficult? (2018)”
As a non-mathematician, I found the Numberphile video on YouTube very helpful for breaking down the basics of Navier-Stokes equations in a very easy to comprehend way: [this video]
Recommends dagw · 2021-08 · Hacker News · on “Tesla valve”
When it comes to fluids (and gases) the keyword you are looking for the the Navier-Stokes equation. In most cases gases and fluids can be handled essentially the same way. There is pretty a good video introduction to Navier-Stokes here: [this video] (part 1) and [LINK] (part 2) The big 'problem' with fluid dynamics is that from the equations it looks like a really simple problem. The Navier-Stokes equation is a couple of lines and you can explain it to a reasonably smart high school student who has taken calculus. And in the 'easy' case where you assume laminar flow and no turbulence it is pretty easy. The problem is when you introduce turbulence into the system then it becomes basically unsolvab
Recommends o4c · 2026-09 · Hacker News · on “On the Navier–Stokes Millennium Prize Problem”
Resources: YT playlist on Millennium Prize Problems By Harvard math department in March 2026 [LINK] On Navier-stokes problem definition: [LINK] [this video] [LINK]