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

  Рет қаралды 446,546

Aleph 0

Aleph 0

4 жыл бұрын

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.
---
Official Problem Statement:
www.claymath.org/millennium-p...
A very informative talk by Dr. Edriss Titi:
• Mathematics of Turbule...
---
Follow me!
Twitter: / 00aleph00
Instagram: / 00aleph00
Facebook: / 00aleph00
__
Music Info: Documentary - AShamaluevMusic.
Music Link: www.ashamaluevmusic.com

Пікірлер: 613
@LostAlienOnEarth
@LostAlienOnEarth 3 жыл бұрын
Why didn't Navier and Stokes solve their own equations, damn it?!
@archockencanto1645
@archockencanto1645 3 жыл бұрын
😂
@ihato8535
@ihato8535 3 жыл бұрын
They did. But the margin was too small.
@kartikkalia01
@kartikkalia01 3 жыл бұрын
@@ihato8535 lmao
@maxwellsequation4887
@maxwellsequation4887 3 жыл бұрын
@@ihato8535 you are a Legend
@neosokretes
@neosokretes 3 жыл бұрын
Run out of paper 😀
@nickmyers4681
@nickmyers4681 3 жыл бұрын
I’ve discovered a truly marvelous solution to the Navier-Stokes equation, which this comment is too narrow to contain
@rjthescholar177
@rjthescholar177 3 жыл бұрын
Publish it, then.
@sthamansinha243
@sthamansinha243 3 жыл бұрын
@@rjthescholar177 You missed the reference.
@nickmyers4681
@nickmyers4681 3 жыл бұрын
@@rjthescholar177 en.m.wikipedia.org/wiki/Fermat's_Last_Theorem
@bramilan
@bramilan 3 жыл бұрын
😄
@rituparn1
@rituparn1 3 жыл бұрын
Myers Last Solution
@ayushthapliyal2462
@ayushthapliyal2462 3 жыл бұрын
The best video on navier-stokes equation
@Aleph0
@Aleph0 3 жыл бұрын
Thank you!! Really appreciate it :)
@DJVARAO
@DJVARAO 3 жыл бұрын
Indeed
@jivanvasant
@jivanvasant 3 жыл бұрын
Ayush Thapliyal > Math as Theology = Sacred Geometry? [6:54 -- 7:01] Aleph Zero: "In a very secular sense, one can say: To know Navier-Stokes is to know the mind of God."
@DJVARAO
@DJVARAO 3 жыл бұрын
@@jivanvasant “Mathematics is the language in which God has written the universe” ― Galileo Galilei
@aVoidPiOver2Rad
@aVoidPiOver2Rad 3 жыл бұрын
Nah bro. This video ist dogshit in comparison to the Numberphile Video
@coolhersheys
@coolhersheys 3 жыл бұрын
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.
@VeteranVandal
@VeteranVandal 2 жыл бұрын
You look tense in your profile pic. Get those tensors out of your life man!
@theludvigmaxis1
@theludvigmaxis1 2 жыл бұрын
I also specialize in fluid dynamics and concur this video is wonderful.
@reimannx33
@reimannx33 2 жыл бұрын
@@theludvigmaxis1 yeah, I specialize in spotting the specialists who fake it.
@pipi0290
@pipi0290 2 жыл бұрын
I'm also a fluib dynansmicsist and it's ok
@primenumberbuster404
@primenumberbuster404 Жыл бұрын
As a Food dinomasochist I can relate.
@z-beeblebrox
@z-beeblebrox 3 жыл бұрын
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)
@mranonymous2729
@mranonymous2729 3 жыл бұрын
I agree with you completely and what beautiful way did you use to present that haha
@Moodboard39
@Moodboard39 5 ай бұрын
Cuz is from God ...
@BYJUSExamPrepGateEseEEECINCS
@BYJUSExamPrepGateEseEEECINCS 3 жыл бұрын
Hey I must appreciate ur work behind d screen..good job👍👍
@Mohd53000
@Mohd53000 2 жыл бұрын
😅😅
@MattT33L
@MattT33L 3 жыл бұрын
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.
@michaelmello42
@michaelmello42 Жыл бұрын
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.
@wejt5454
@wejt5454 Жыл бұрын
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
@12jgy
@12jgy 4 жыл бұрын
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?
@Aleph0
@Aleph0 4 жыл бұрын
Couldn't agree more! The simplest equation becomes unsolvable once applied to fluids. It's crazy that we can't solve even the most basic non-linear PDE's; it shows just how far we need to go in understanding nature mathematically. I might make a video on some other DEs: likely the Einstein Field Equations of General Relativity (tensor calculus on curved manifolds, very interesting), or maybe the three-body problem. Thanks for the comment!
@carloserazoramirez4286
@carloserazoramirez4286 3 жыл бұрын
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
@almalucia2650
@almalucia2650 7 ай бұрын
Thanks for the great video. I have watched a handfull of videos to understand the Navier Stokes equation, and yours is the first one that actually managed to teach me something about it.
@oot007
@oot007 2 жыл бұрын
This is the best explanation of Navier Stokes I've seen. Well done.
@HadiM-rb7yo
@HadiM-rb7yo 3 жыл бұрын
i'm really happy i discovered this channel
@Aleph0
@Aleph0 3 жыл бұрын
I'm glad too! Welcome.
@playerscience
@playerscience 3 жыл бұрын
I have no words to describe......... How beautiful this explanation was......
@luk45ful
@luk45ful 3 жыл бұрын
This is definitely the kind of content I was looking for! So good!
@HitchHawk
@HitchHawk 3 жыл бұрын
These videos are amazing!! I really love the presentation along with the explanations. Phenomenal work dude!
@OwenMcKinley
@OwenMcKinley 4 жыл бұрын
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
@Aleph0
@Aleph0 4 жыл бұрын
Thank you!! That's very kind :) I try to show the core intuition behind the topics when making these videos.
@ATlantis12
@ATlantis12 3 жыл бұрын
Bro he didn’t explain anything about the mathematics of the equation u simply found the explanation U were looking for to the degree of difficulty that U were looking for but this is simply a history lesson on the problem
@OwenMcKinley
@OwenMcKinley 3 жыл бұрын
@@ATlantis12 Where in my comment did I indicate that I felt as though I understood the massive scope of this problem with an elite level of precision? It's enjoyable to watch a well-made, digestible presentation on these enormous math problems; nothing more, nothing less.
@rumfordc
@rumfordc 3 жыл бұрын
@@OwenMcKinley you indicated it at the words "not far away"
@OwenMcKinley
@OwenMcKinley 3 жыл бұрын
@@rumfordc Ah, perhaps; I agree. But I don't believe that I understand the full scope of the problem. There's a reason why it still hasn't been cracked.
@davidmyers7508
@davidmyers7508 3 жыл бұрын
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.
@faizanka5088
@faizanka5088 3 жыл бұрын
Wow, that was beautiful explanation of navier stokes equation. This channel deserves more attention
@kirach3734
@kirach3734 Жыл бұрын
for the very first time in my life...i feel alive after watching this video....wow thank you
@Bton0711
@Bton0711 3 жыл бұрын
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!
@apexmcboob5161
@apexmcboob5161 3 жыл бұрын
You are a superb teacher. I've subscribed and as soon as I finish typing this I'll search for all your other videos. Thank you!
@BHAVYAMATHURBEE
@BHAVYAMATHURBEE 3 жыл бұрын
Dude. Awesome. Keep doing what you do. Ill be watching your future with great interest.
@juanfelipe9983
@juanfelipe9983 3 жыл бұрын
Just Woww!!! It was quite simple for You to explain the problem behind Navier-Stokes equations!! Congrats!!
@michalfishkin9200
@michalfishkin9200 3 жыл бұрын
I am so happy to see Ladyzhenskaya's work mentioned here! Excellent video, as always.
@AlexMoophty
@AlexMoophty 2 жыл бұрын
You are simply amazing! Pls keep going with your content🔥❤️
@mariaameddah5983
@mariaameddah5983 3 жыл бұрын
Damn this is like the best video I have seen about this topic, very well explained. Thank you!
@mmsrkmax5820
@mmsrkmax5820 2 жыл бұрын
I have been studying fluid dynamics for last 7 years and I must say this presentation was spot on!!! Great job!!!!
@AnakinSkywalker-zq6lm
@AnakinSkywalker-zq6lm 2 жыл бұрын
I’ve been studying fluid dynamics for the past 7 minutes. And it’s true!!!
@AndrewPa
@AndrewPa Жыл бұрын
I study it for 25 years and can say it is mathematical point of view on physical problem.
@jackl331
@jackl331 3 жыл бұрын
soooooooo moved by your fascinating presentation...... mind blowing... thx
@starstuff11
@starstuff11 Жыл бұрын
I am so glad I found this channel!
@Chill----
@Chill---- 3 жыл бұрын
Yep I also agree that your channel is gonna boom. I liked the channel after finishing my very first video from this channel.
@anirudhsingh3507
@anirudhsingh3507 2 жыл бұрын
One needs a certain level of passion to make such video!!!!! Thanks man , it was a great! explanation.
@Manjeetemo
@Manjeetemo 3 жыл бұрын
Really nice video on Navier-stokes eqn. Will be waiting for furthur uploads..Keep it up dude.
@PinakiSwain
@PinakiSwain 2 жыл бұрын
Thanks for sharing this. A very accessible presentation of a complicated equation.
@gauravs3566
@gauravs3566 3 жыл бұрын
Really love your work bro! Keep it going
@PacoOtis
@PacoOtis 2 жыл бұрын
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.
@reimannx33
@reimannx33 2 жыл бұрын
Yeah, my ancestor proved your ancestor tried to pull a failed hoax. So, you inherited a failure. So, how it feel to walk into a bar knowing that the ladies think you inherited a failure ? :)
@EmilM-pb2hn
@EmilM-pb2hn 2 жыл бұрын
@@reimannx33 My ancestors of vikings made your ancestors beg for their lives. So, how does it feel to walk into a bar knowing that the ladies think you're a weak beta male?
@reimannx33
@reimannx33 2 жыл бұрын
@@EmilM-pb2hn Civilized intelligent Man may be physically weaker than the brutes and beasts, but it is our wits and IQ that led us to the moon, and create science & technology rather than the reptilian-brained brutes. So, while you may flout your low IQ and drum your empty cranium to make noise, the rest of the world laughs at your folly characterised by ignoramus being your "Dream"y bliss.
@cara-setun
@cara-setun 2 жыл бұрын
My ancestor made a song that almost no one cares about anymore but was featured in an old movie, so that’s cool 😎
@IODell
@IODell 3 ай бұрын
@@cara-setun We might be related.
@michaelcollins7192
@michaelcollins7192 3 ай бұрын
Brilliant short video, well done! I'd like longer ones too.
@rousselrobin6060
@rousselrobin6060 3 жыл бұрын
Loved the video! This made me realize that there isn't much vulgarisation content on youtube about functional analysis and pde theory compared to topics like algebra and topology. I'm guessing that might be because the subjects seem to deal on the surface with relatively easy topics like multivariable calculus, and it feels hard to go into more details without getting into the specifics of various functional spaces. That's a shame because these are the fields I study and it sometimes kind of feel like they're unappreciated by "pure" mathematicians. If you want to talk more about this kind of stuff, I think it would be really cool to have a video on distribution theory. I feel like the concept might be general enough to fit into one video, more so than sobolev spaces for example.
@nelsonpereira9306
@nelsonpereira9306 3 жыл бұрын
I really appreciate your videos! Hope you keep on.
@imaduddinalawiy3426
@imaduddinalawiy3426 3 жыл бұрын
you explained everything so clearly, thank you
@Aleph0
@Aleph0 3 жыл бұрын
thanks so much!
@atil4
@atil4 3 жыл бұрын
A part from being among the top top channel of math in all KZbin, there is something special about yours the way you simplify the key milestones to really understand a hard concept. Without the need of big animations, because it relays on these key Simplifications. As you side in other video; you are simplifying knowledge for us, thank you for sharing this digested math wisdom. I loved all your videos so is silly to suggest but I really calculus since is the language of Nature. Understanding the nature of calculus is understanding nature from Math point of view. I would love to see more related video to differential equations e.g. Laplace transformation. Or the relation between different fields of math. One subject that always fascinate me is the conical curves :) This channel can only grow, thank you for your efforts.
@cchakrapani3574
@cchakrapani3574 4 жыл бұрын
Brilliant. This is totally awesome. Way to go, Aleph!
@Aleph0
@Aleph0 4 жыл бұрын
Thanks uncle!! That's very kind of you :)
@farhanfuad6045
@farhanfuad6045 2 жыл бұрын
Your explanation, presentation, comparison with nature life god everything...everything is awesome
@osemudiame123
@osemudiame123 4 жыл бұрын
Best of luck getting this Chanel up and running
@Aleph0
@Aleph0 4 жыл бұрын
Thank you!! Appreciate it :)
@mauriciougaz
@mauriciougaz 3 жыл бұрын
Beautiful and outstanding job man!
@kenkiarie
@kenkiarie 2 ай бұрын
Thank you for this! Very intriguing.
@rohlay00
@rohlay00 3 жыл бұрын
Came here to procrastinate on my upcoming fluid mechanics exam. Wasn't expecting such a philosophical ending.
@evelocz
@evelocz 3 жыл бұрын
Great work!! Keep shining brother!
@nathanbarnard7896
@nathanbarnard7896 3 жыл бұрын
I've just started working on fluid mechanics, it's nice to see where it's leading, even if it's leading somewhere unsolvable :))
@luizcarlosf2
@luizcarlosf2 3 жыл бұрын
Very inspiring video... Wish I had a calculus teacher like that.
@albertora4391
@albertora4391 3 жыл бұрын
Congratulations! Nice and complete video!
@harryh5666
@harryh5666 3 жыл бұрын
Awesome vid. Would be great to have some more Millennials explained simply like that
@joeljacob2234
@joeljacob2234 3 жыл бұрын
Just beautifully put together!
@Aleph0
@Aleph0 3 жыл бұрын
Thanks Joel!
@hopkinsyb4306
@hopkinsyb4306 3 жыл бұрын
Great vid hope you do one for every million dollar question
@parkashsingh9044
@parkashsingh9044 3 жыл бұрын
wow.. one of the best.. keep it up bro.. 👍👍
@Shroomssss
@Shroomssss 3 жыл бұрын
Really great video! But Navier stokes also has its limits! Even for fluids. You can only apply them to continuums where the Knudsen number is small enough.
@tkguha6918
@tkguha6918 11 ай бұрын
Excellently done.
@norlan718
@norlan718 3 жыл бұрын
This is an excellent video. Keep it up.
@austinkmhi
@austinkmhi 3 жыл бұрын
I absolutely have no knowledge on physics but I understood this...kudos man
@AlexAnteroLammikko
@AlexAnteroLammikko 6 ай бұрын
Im not a physicist at all, I don't even study physics, but work in healthcare and have a question on what an "initial condition" is and what "all eternity" means in the context of these equations. I assume this is undergrad level stuff (not the solving the equation, but those particular terms) so am sure some people in the comment can help. Basically, if I have a container of water like a bucket, and the water is settled, and thenI punch it, there is now an "initial condition". But any calculation of the resolving of that reaction can't, and won't, take into consideration other outside acts like me throwing in a brick or tipping the water over or rain occurring. Now lets take the Ocean, or the "air" (the various spheres the names of which I can't recall now but all of which interact with each other). All of these are complex systems with various dynamic entities in them. The Ocean isn't a closed system but even if it was and no water escaped and no additional creatures went in, the existence of animals that can "randomly" change directions would greatly interfere with the calculations as they create new flow. So is the equation assuming a perfect closed system and, if so, what value, if any, does solving the equation have for the "real world" (I have a friend in mathematics who hates the " real world" question but I am not in mathematics so ill ask it :p )
@sergiolucas38
@sergiolucas38 2 жыл бұрын
Great video, so much quality :)
@72saurabhsen73
@72saurabhsen73 3 жыл бұрын
Wonderful job 👍
@Kurd05
@Kurd05 2 жыл бұрын
Do a video on mass gap bro! You explain the millennium problems so well
@phuongly7811
@phuongly7811 3 жыл бұрын
the best video about the Navier Stokes Equation. "Solving Navier Stokes Equation is like solving a personality" ...wow
@AJ-et3vf
@AJ-et3vf 2 жыл бұрын
Awesome video. Thank you!
@thunder852za
@thunder852za 3 жыл бұрын
Navier stokes in incompressible form hurts my eyes - detracts from the problem - and I mainly work with incompressible flows. In any case, great video and very well presented.
@luofenghuang8015
@luofenghuang8015 3 жыл бұрын
Very nice presentation! You can add a new episode on how to solve the equation numerically.😊
@kirstenwilliams6056
@kirstenwilliams6056 3 жыл бұрын
Brilliant, clear and interesting introduction to this topic - thank you!
@bythetimeyoufinishedreadin9083
@bythetimeyoufinishedreadin9083 3 жыл бұрын
I'm a second year in aerospace engineering, and this was very interesting to watch. Super stoked to learn more about this in further detail (no pun intended)
@LostAlienOnEarth
@LostAlienOnEarth 3 жыл бұрын
Best math channel ever
@DragonRazor9283
@DragonRazor9283 3 жыл бұрын
Holy shit.... this made me think and perceive things differently
@DaMonster
@DaMonster 3 жыл бұрын
Awesome video
@ratboy_
@ratboy_ 2 жыл бұрын
Very well done
@shahryarhabibi7187
@shahryarhabibi7187 3 жыл бұрын
thanks a lot- very good job
@sureshdeshpande6281
@sureshdeshpande6281 Жыл бұрын
Very good. Thanks a lot.
@teriyaki8643
@teriyaki8643 3 жыл бұрын
Beautiful!
@mandernachluca3774
@mandernachluca3774 3 жыл бұрын
This started like 100 Second Physics, went on like Today I Found Out and ended like VSauce. XD
@JohnRobertPotter
@JohnRobertPotter 3 жыл бұрын
Excellent content, subbed and liked
@soulintent4129
@soulintent4129 2 жыл бұрын
Amazing video ⭐❤
@maxs5022
@maxs5022 3 жыл бұрын
best math youtuber i know!
@tamilolidurai6043
@tamilolidurai6043 2 жыл бұрын
BESTEST Video ever in internet about N.S equations. Million thanks for this. Also, Solutions for N.S. equations doesn't exist like the word BESTEST :)
@ClemoVernandez
@ClemoVernandez 3 жыл бұрын
Amazing video! you deserve more subs
@Aleph0
@Aleph0 3 жыл бұрын
Aw thanks! That's really sweet :)
@kylevandeventer1037
@kylevandeventer1037 2 жыл бұрын
Wow… I just graduated with my math degree and I believe you’ve just convinced me to go back for phd… dang it
@bobtree4583
@bobtree4583 3 жыл бұрын
Wow. What a video!
@mattytavares
@mattytavares 3 жыл бұрын
Amazing channel!
@jostpuur
@jostpuur 2 ай бұрын
From where do you get the time derivative of the pressure? It doesn't appear in Navier-Stokes equations.
@teguhimanwidodo77
@teguhimanwidodo77 3 жыл бұрын
I love the last quote
@sudheerv6941
@sudheerv6941 3 жыл бұрын
can you please make a video on curl, divergence and electromagnetic equations. intuition behind those concepts is elusive for me
@pravinkolhe82
@pravinkolhe82 Ай бұрын
Enjoyed!
@finnbraaten3264
@finnbraaten3264 11 ай бұрын
I think we should be a bit careful. Navier Stokes does not describe everything that flows. It only describes flow of even viscosity, isotropic media. It would not describe nematics, polymer flow, or that of active matter/odd viscosity media.
@pollutedwaters8126
@pollutedwaters8126 2 жыл бұрын
Awesome video.
@AryanSingh-og7ke
@AryanSingh-og7ke 3 жыл бұрын
A pattern to noticed in likes and dislikes, likes can be described as squares and dislike as sum of squares Like : n^2 Dislike : (n+2)^2+(n-1)^2
@eriktempelman2097
@eriktempelman2097 3 жыл бұрын
Excellent video.
@tharollodikgale
@tharollodikgale 3 жыл бұрын
Nice Presentation
@beauthetford7608
@beauthetford7608 3 жыл бұрын
nice video aleph naught!
@nirmalya_nanda
@nirmalya_nanda 3 жыл бұрын
The most amazing explanation and video on navier stokes Btw what and where do you study
@aaryanbudhirajamusic6874
@aaryanbudhirajamusic6874 3 жыл бұрын
Amazing video!
@alanmakoso1115
@alanmakoso1115 2 жыл бұрын
THis teaches everything that's needed
@abstractnonsense3253
@abstractnonsense3253 3 жыл бұрын
Great video
The million dollar equation (Navier-Stokes equations)
8:03
vcubingx
Рет қаралды 470 М.
Navier-Stokes Equations - Numberphile
21:03
Numberphile
Рет қаралды 1,1 МЛН
Когда на улице Маябрь 😈 #марьяна #шортс
00:17
Did you find it?! 🤔✨✍️ #funnyart
00:11
Artistomg
Рет қаралды 121 МЛН
Normal vs Smokers !! 😱😱😱
00:12
Tibo InShape
Рет қаралды 117 МЛН
Understanding Bernoulli's Equation
13:44
The Efficient Engineer
Рет қаралды 3,2 МЛН
Millennium Problems: Math’s Million Dollar Bounties
15:05
Sideprojects
Рет қаралды 149 М.
The bridge between number theory and complex analysis
9:59
Aleph 0
Рет қаралды 195 М.
Understanding Laminar and Turbulent Flow
14:59
The Efficient Engineer
Рет қаралды 943 М.
Fluid dynamics feels natural once you start with quantum mechanics
33:00
Navier-Stokes Equation Final Exam Question
14:55
Fluid Matters
Рет қаралды 106 М.
Stokes' Theorem on Manifolds
6:19
Aleph 0
Рет қаралды 171 М.
This is why you're learning differential equations
18:36
Zach Star
Рет қаралды 3,3 МЛН
Когда на улице Маябрь 😈 #марьяна #шортс
00:17