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Exploring the Million-Dollar Navier–Stokes Problem

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Tags: mathematicsphysicsdifferential-equationnavier-stokes-equations

One of the hardest puzzles in both Mathematics and Physics is to solve the Navier-Stokes Equations. These equations describe the behavior of fluid and form the foundation of fluid dynamics. They are not only essential for realistic fluid simulations in games and movies, but also play a crucial role in predicting turbulence in air, cyclones, and even the weather patterns. Even proving that whether a correct solution exists or it blows up to infinity would be enough to win the million dollar prize. But, why are the Navier-Stokes equations so hard and difficult to solve? why does this happen? In this video, you and I are gonna explore one of the three strategies proposed by Terence Tao as a possible path to tackle such a problem.

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6.45 Overall score*

58 Rank

14 Votes

6 Comments

Comments

5.4

The video was generally solid, but some things appeared on screen for such a short time that I had to keep pausing. Very instructive video, but having to pause and rewind was a little frustrating. This is something that can be mastered with practice, so I would love to see you hone the timing in coming videos.

Just a bit boring. Looking at equations isn’t that exciting

Very understandable! I would have appreciated a visualization of individual moving particles to help better make sense of the advection and diffusion terms and how the neighboring particles’ velocities affect a particle’s velocity.

8.2

Very nicely done! It’s not easy to make an accessible video that actually makes me feel like I’ve learned something about a technical research area like Navier-Stokes, but this did! Great job. Some of the animations (especially with text) were a bit sloppy or quick though, and I really didn’t get the star people… but otherwise it was great!

Very interesting video. I know you wanted to focus on the mathematical point but for some concepts such as the critical quantities, it would be very helpful to have at least some kind of physical interpretation (for example what does it actually mean, when the kinetic energy at some point ‘blows up’).

The part by part breakdown of Navier Stokes was good