A Brief History of the Navier-Stokes Equations

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From Isaac Newton to Terrence Tao.

[@engineer_leo]

Check out our course in Udemy about the Navier-Stokes equations: www.udemy.com/understanding-the-navier-stokes-equations/

[@aditya234567]

Link not working!!

[@bhangrafan4480]

Amazing, getting Arnold Schwarzenegger to narrate your video.

[@engineer_leo]

lmao

[@ozzyfromspace]

I solved the Navier-Stokes equations in n-dimensions on a tissue during a 10 minute bathroom break when I was 5, but I used said tissue so my brilliance went unrecognized. I’d replicate my work, but I’m really busy.

[@capuccinolight]

Float Circuit Great! Now: Could you help this guy improve his accent so we can all understand anything?

[@engineer_leo]

@@capuccinolight Hey guys, take easy on me. I'm not a native english speaker. I'm trying my best to improve my accent issue on the more recent videos. Go check it out. Cheers

[@ratchetguns]

He's perfectly understandable to me

[@td866]

@@capuccinolight supongo que tu y tu familia tienen accento "espanol" cuando hablas ingles que qualquier gringo pueda reconocer. por favor, pierdalo para que hables correcto!

[@td866]

@@capuccinolight i understand him fine. maybe you're not a native english speaker! i'm glad he made a great video.

[@juliusrobertoppenheimer9104]

This video is several months old and youtube just shoved it in my feed today, but im glad it showed up

[@camembertdalembert6323]

I have a solution to the Navier-Stokes equations but there is not enough space in the margin to write it. Please send the million dollar prize now.

[@zeroethsort1071]

LOL I love this so much

[@datdang9113]

Although the Navier-Stokes equation is the heart of basic fluid mechanics, I haven't really understood it. In order to solve it in engineering problems, you have to use boundary conditions: no slip, etc. to simplify it, and by simplify, I mean getting rid of most parameters in the equations. So I can't imagine how to really solve all of these.

[@31337flamer]

numerically.. there are methods called FDM (Finite Difference Method) FVM (Finite Volume Method) and FEM (Finite Element Method) that can be used to get approx. solutions to differential equations that are widely used in all engineering softwares like solidworks and others :)

[@9wyn]

Thank you for sharing this informative history. 🙏

[@jayakrishnanm7838]

Really cool video leo .. hope you make more of them !! 😀

[@spacemanspiff7638]

Great content. Eagerly waiting for the next one.

[@engineer_leo]

Thank you very much!

[@ehsanheshmati5842]

One of the greatest explanation of history of the N.S. equations. Thank you Leo.

[@engineer_leo]

You're welcome!

[@karthivenkat6636]

Really a great video. Thank you for sharing this wonderful information. I'm Subscribed!!!

[@peregrineflow7354]

Thank you for this information. This was exactly what I was looking for. New subscriber.

[@engineer_leo]

Thanks for the sub!

[@georgemurphy4950]

Excellent video. Thanks for your work

[@Ace-Maverick]

Excellent video!! I just subscribed!

[@joshlarson407]

The greatest video man has ever made.

[@gabitheancient7664]

krl mano eu reconheci q tu era br pelo seu sotaque, depois fui checar no seu sobre e tu realmente ékk, ótimo vídeo

[@kennettallgren640]

Thank you for this video, well Done!

[@suryakiran]

awesome work leo

[@aion2177]

very beautiful video :) thank you :)

[@matheus4885]

Very nice video!

[@Ivan_1791]

You have a new subscriber. :)

[@raphango]

Great video! Thank you! God bless you! 🙏

[@inotmark]

Nice introduction! THank you.

[@user-gk6dt2nf4h]

Thank you!

[@ahmetkirhan5896]

Thank you so much for this video sir :)

[@siddharthnaik608]

This is a good video for anyone who wants to get some clarity of the Navier=Stokes Equation. 😁

[@littlebeni295]

Love the content

[@joyboricua3721]

I personally would not say the equations govern the phenomena, but describe it.

[@paulgraf6963]

Awesome video, thanks!

[@engineer_leo]

Glad you liked it!

[@timothystudies2753]

where to find the chart at 4:00 ?

[@ThomasJr]

Thanks Engineer Leo. What is the asterisk in 2016* for?

[@thomasparker4109]

Please, what the song play on background at the end?

[@yash1152]

4:20 - 4:57 I am a high school student, and am trying to understand what "Navier-Stokes Existence and Smoothness" problem really means i.e. what is the actual problem here. So, foll are some of my questions: 4:15 4:43 what does "solution to the problem" mean here?? Like in a function, the solution mean what input would satisfy the problem, so if this analogy is still relevant here, then what are the input parameters here?? {just realised i am running out of time, so, will ask other questions some day later maybe}

[@cull7096]

The problem here is that you're not sure that if u input numbers in the N.S equations to solve it there is always solutions and if they're solutions they need to be realistic

[@AviatorJosh]

Check out this link: www.grc.nasa.gov/www/k-12/airplane/nseqs.html. I’m impressed that you are interested in such high level subject matter as a high school student. Unfortunately, the rigor of the mathematics used in solving the Navier-Stokes equations (partial differential equations) is typically taught at the graduate school level in engineering and physics.

[@firstnamelastname8418]

Great video

[@engineer_leo]

Thanks!

[@stylshe.]

Great vedio

[@compoundconfidence3329]

Love it!

[@engineer_leo]

So glad!

[@mrkps1986]

that is amazing, its helpful in India

[@yash1152]

1:32 didnt know its complete name is "Galelio" law of inertia. 👍 3:00 mathematical fluid dynamics vs engg hydrodynamics

[@rohitbarman3765]

Very useful content.. I am an undergrad Chem engeering student and want to get into simulating fluid flow. Can you suggest how to get started? Thank You.

[@engineer_leo]

Take a look Ansys free course at edX. They teach the basics of CFD, along with Fluent. You can also learn openFOAM, which is an open-source and free simulation software.

[@allandavis6116]

There are a number of vids on the subect, e.g. kzbin.info/www/bejne/d2OlgaSdlNmofqs

[@Devanshgupta]

Thanks

[@engineer_leo]

Welcome!

[@spyrex3988]

I love your name, Leo

[@AtomicusPrime]

How did you make the chalkboard graphics? Or were they taken from elsewhere?

[@engineer_leo]

Free stock videos on youtube

[@yash1152]

oh okayy, talking about 3:08 yeah, i like them too. I wish to be able to make smth like these some day 😅:wishful_thinking:

[@davidortega264]

That black magic from the minute 2:53 is real?

[@engineer_leo]

Lol it is a free stock video on youtube

[@yash1152]

lol

[@mkim2728]

what is different between N-S equ. and Rheology ?

[@engineer_leo]

Rheology studies the constitutive relations regarding the stress tensor. N-S describes generally newtonian fluids.

[@su2m86sp]

be consistent and i will bring 40 subscribes from my class

[@engineer_leo]

I'd really appreciate that! Thanks!

[@jeremyschaeffer7316]

What is that going on at 3:00 ???

[@engineer_leo]

Black magic

[@immanuelwashere2]

Are you on Twitter? I love this. I want to share w/ credit

[@engineer_leo]

Yes. It's twitter.com/engineer_leo

[@msc-gm4qh]

From the Beginning i was only thinking of Terence Tao

[@engineer_leo]

I believe he is the scientist who made the most relevant advances in the mathematical understanding of the Navier-Stokes equations recently.

[@PaulPukite]

@@engineer_leo Tao was working on shallow-water wave approximations to Navier-Stokes. terrytao.wordpress.com/2011/03/13/the-shallow-water-wave-equation-and-tsunami-propagation/ I took a different approach and simplified the equations even further for the topological constraints along the equator

[@arvind31459]

"Navier-Stokes governs the movements of these fluids" 🙄 It should be Navier-Stokes equation satisfy their movements.

[@yash1152]

yeah, i was thinking same.

[@Ottmar555]

I much prefer the Cauchy momentum equation.

[@jamiegoddard2495]

You need a better mic, then this would be top quality info.

[@engineer_leo]

I bought a new one. Check out the newest videos :)

[@tronghai55]

The Navier stokes equation as its formula is incomplete cause it does not take in consideration the factor of the speed velocity of the fluid. Since 3 differential numerators variables are by factor of a constant. That constant can be positive or negative to which has to obey to the mechanic constant of the specific viscosity flow rho. The factor limit of the constant fluid viscosity will determine its sub integral of the k of the Navier stokes formula. I might be wrong for these assomptions for the formula is incomplete.

[@utkarshpuri3739]

Don't know why I'm watching the video on its original speed...😂

[@ribaldi]

So unproven but applicable? How is an equation not proven is seemingly reliable?

[@engineer_leo]

It is reliable in a sense that it is physically proven and validated for numerous experiments, both physical and numerical, for the restrictions mentioned (incompressible, newtonian, etc). This equation is not proven to have solution, smoothness and uniqueness mathematically, which would provide more rigorous background for mathematical treatment of these equations.

[@cristianpistacchio]

That is called postulate, there are a lot of them, like the 7 problems and fourier postulate for heat trasmission

[@noble2694]

watch in 1.5x speed. thanks me later.

[@matron9936]

Are you German speaking?

[@engineer_leo]

My native language is portuguese, but I know some german.

[@ylmazylmaz222]

listen on x1.5 thx me later

[@user-sq5hv9tj3i]

I'm pretty sure most people who want to know about naiver-stokes equation has already been familiar with Newton and his achievements, so no need for those

[@amirsafari7140]

Crapppppy mic

[@OOoKarmaoOO]

You need to pronounce better