Talk:Navier–Stokes equations

Most important case missing

The Navier-Stokes equation for the case of a Newtonian incompressible fluid are used by more than 90% of researchers in the field. That this case is not given at all is likely to confuse many students and lead them to think that this article is irrelevant to their research (or aimed at irrelevant special cases).

I strongly suggest adding these simplfied forms early-on in the article.

why? the special forms are just that, special forms. And if you want the newtonian incompressible case, just add it: it is trivially the conservation of momentum plus incompressibility, expressed as:

$\nabla\mathbf{v}=0$

which you would easily get from the article.

on the other hand, the compressible equations take way too much space :)CyrilleDunant 06:51, 3 November 2006 (UTC)

My point is: if 90% of the people coming to this page are needing the Newtonian incompressible form -- and that is missing -- one has a article well suited to 10% of those who come looking. Water, air, salad dressing, usually at low Mach number, these are the fluids of life and most technology. When you suggest "just add it" I'm unsure if you would like me to proceed to edit the article. -- best wishes -- User:Lathrop 21:31, 3 November 2006 (EST)

Well, this is WP! Of course you should edit the article if you think information should be added! I will just note that need is perhaps a bit of a strong word for a set of equations...CyrilleDunant 09:58, 4 November 2006 (UTC)

Hi, congratulations to all for the nice work. I just revised the "incompressible" section, perhaps that is what you wanted. But I feel that the rest of the page still needs some rewrite. I kept the full equations with all components etc... I know that students find them very useful. For Cyrille, "need" is how we teachers see some very useful pieces of math, we sense that students and users of science "need" the equations. You cannot do this type of science or engineering without them. Zaleski 23:54, 6 February 2007 (UTC)

Thank you Stéphane, that is a very useful improvement. —Preceding unsigned comment added by Lathrop (talk • contribs) 22:34, 1 December 2010 (UTC)

- dear fellow, what about the creeping/laminar flow liquid by special long chain molecules in water dissolved and called "creeping-fluid" being an additivum for slippery gliding over Navier-Stokes surfaces? This expression (creeping-fluid, contracted from: creeping chain molecules in water dissolved and constituing an extremely slippery fluid for gliding thru tubes and pipes without any rest of friction that could otherwise be caused by the surface passed by or slipped over) was coined in the eighties of the past century, it has been applied also by the New York fire brigades in the harbour and the water that contained the "creeping molecules fluid" reached a distance one-third wider than before when without that additivum of the so-called "creeping-fluid". The flexible pipe itself therefore is almost lubricated from inside, and the molecules in long chains of the water did flow, as if they would draw each other outside and they slipped without the slightest resistance, neither by the tube inner surfaces nor by themselves when advancing - under the same pressure as before - but getting a considerably higher speed. -- What ist the meaning of the scientists with regard to this, concerning the Navier-Stoke surface layer theory? - Yours sincerely, bluaMauritius. —Preceding unsigned comment added by 84.62.236.125 (talk) 08:32, 21 May 2011 (UTC)

Maxwell's Equations Analogy

There's an analogy between the Navier–Stokes equations and Maxwell's equations. It would be good to have a brief section explaining this analogy. JKeck (talk) 05:08, 3 June 2010 (UTC)

Jormakka

It's been solved! http://ejde.math.txstate.edu/Volumes/2010/93/jormakka.pdf --188.220.102.130 (talk) 23:08, 21 August 2010 (UTC)

The Millennium Prize problem related to these equations might have been solved. Until the paper you linked has been reviewed by others, and third-party sources have reported this, we shouldn't be reporting that the problem has been solved. In any case, we have a separate article, Navier–Stokes existence and smoothness, specifically for the Millennium Prize problem formulation, and any discussion of this should go there. — Gavia immer (talk) 01:50, 22 August 2010 (UTC)

Convection vs advection

This talks about convective acceleration when it should talk about advective acceleration.

Convection implies that the flow is buoyancy-driven in some way, while advection refers to tracers (eg temperature/momentum) being carried with the flow. —Preceding unsigned comment added by 150.203.10.73 (talk) 06:41, 6 April 2011 (UTC)

For a previous discussion on this: see Talk:Navier–Stokes equations/Archive 1#Convection Vs Advection. -- Crowsnest (talk) 13:39, 6 April 2011 (UTC)

Where are the equations?

This article has a good description of the uses, derivation, and applicability of the equations, but ironically does not label the equations themselves clearly. I assume the most general form is this equation in the 'Derivation and description' section:

$\rho \left(\frac{\partial \mathbf{v}}{\partial t} + \mathbf{v} \cdot \nabla \mathbf{v} \right) = -\nabla p + \nabla \cdot\mathbb{T} + \mathbf{f},$

except that it is not labelled the "Navier-Stokes equation" but rather the Cauchy momentum equation, Could someone please clarify this? Cheers --Chetvorno^TALK 22:14, 10 April 2011 (UTC)

Because as such, it is not complete: it further requires a constitutive relationship (which will relate T, v and p). NS is the complete set of equations such that the problem can be (possibly) well-posed.CyrilleDunant (talk) 01:40, 11 April 2011 (UTC)

The Navier-Stokes equations are not complete in general anyway because they only define the momentum conservation. For incompressible flow the continuity equation is needed; and for compressible flow the continuity equation, energy equation, and an equation of state are all required. — Preceding unsigned comment added by 164.107.59.74 (talk) 23:24, 26 May 2011 (UTC)

Give the formula first

Who is writing this article? Give the formula in the very first section and define the variables in it before going for the derivation and other bs. Someone looking for the formula can never find from this article which one is the Navier–Stokes equation. Damn it. 122.176.58.109 (talk) 14:34, 20 September 2011 (UTC)