Navier Stokes Equation | A Million-Dollar Question in Fluid Mechanics

The Navier-Stokes Equations describe everything that flows in the universe. If you can prove that they have smooth solutions, you'll win a million dollars.

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A very informative talk by Dr. Edriss Titi:

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Music Info: Documentary - AShamaluevMusic.

[nickmyers]

I’ve discovered a truly marvelous solution to the Navier-Stokes equation, which this comment is too narrow to contain

[LostAlienOnEarth]

Why didn't Navier and Stokes solve their own equations, damn it?!

[ayushthapliyal]

The best video on navier-stokes equation

[coolhersheys]

As a fluid dynamicist, I congratulate you, sir, for the quality of your videos. You manage to convey the meaning of the topics you present, in a clear and concise manner, and the beauty of mathematics. More content like this is needed. Keep the good work.

[z-beeblebrox]

There's something profoundly recursive about using a fluid simulation to illustrate what aspects of fluid motion prevent us from solving Navier-Stokes...an equation that would allow us to accurately simulate all fluids

(obviously fluid simulations are using shortcuts and it's just for demonstration purposes, but it's still brain twisty)

[BYJUSExamPrepGateEseEEECINCS]

Hey I must appreciate ur work behind d screen..good job👍👍

[HadiM-rbyo]

i'm really happy i discovered this channel

[OwenMcKinley]

Dude, your channel is gonna blow up. Content and presentation is awesome! Really hope to see more from you. You make math feel visceral, not "far away, " if that makes any sense

[jgy]

What I find even more beautiful about Navier-Stokes is that when actually think about it, it arises in a relatively "simple" manner, being Newton's Second Law applied to fluid mechanics, but it still so incredibly difficult. Nonlinear parcial differential equations are so rough to handle, but at the same time they appear in so many places in the study of nature, I guess this is a testament to just how complex nature really is. Anyway, very good video, and a question for you, do you plan on covering any other specific differential equations, and if yes, which ones?

[Bton]

Love the video!
Maybe interesting to know: In CFD (Computational Fluid Dynamics) we solve it by averaging the turbulente fluctuation of the velocity. Therefore different turbulence models are being used and improved every year. That's why flow simulation, around airplanes for example, is possible. So we can't solve it at all, but we became really good at simulating it!

[mmsrkmax]

I have been studying fluid dynamics for last 7 years and I must say this presentation was spot on!!! Great job!!!!

[PacoOtis]

The "Stokes" is an ancestor of mine who developed an equation for the rate of fall of a sphere through a viscous medium. I never have figured out what use the formula was. It's nice to see educational videos and thanks for sharing.

[Mt]

I see that trajectory, well deserved, you'll quickly rise to the top. I love your enthusiasm and passion for the subjects, not to mention the production and execution of the content are top-notch. Hats off.

[carloserazoramirez]

This is one of the most beautiful videos I've seen on youtube. Dude, youre freaking amazing and you've got me subbed so bad

[lukful]

This is definitely the kind of content I was looking for! So good!

[davidmyers]

I just want to gush about this guy's videos to every person in my life. Their quality is singular.

Thank you Arts-and-Crafty Storyteller Math-Man for expending your focus in this way.

[oot]

This is the best explanation of Navier Stokes I've seen. Well done.

[wejt]

when i finally grasp the concept by the end of the video, especially if it ends with such quotes, i get chills down my spine, i love your content

[michaelmello]

It's one thing to understand a difficult subject but quite a different matter to convey one's understanding with this level of clarity. It is a gift.

[HitchHawk]

These videos are amazing!! I really love the presentation along with the explanations. Phenomenal work dude!