Why do the Navier-Stokes equations give us non-existent results for 3D flow?

In summary, the conversation discusses the limitations and challenges of using Navier-Stokes equations to model fluid behavior. The equations have been shown to give incorrect or non-existent results in certain situations, leading to the need for reevaluation and development of more rigorous mathematical methods. However, even if the equations were to be solved, they may not accurately describe fluid behavior at all scales and would still require approximations. The conversation also touches on the concept of turbulence and the difficulty of obtaining detailed solutions due to computational limitations. Overall, the discussion highlights the complex relationship between mathematics and physics, and the ongoing efforts to improve our understanding of fluid dynamics.
  • #1
Jurgen M
Navier-Stokes equations for 3D flow gives us wrong/non existent results, results that don't exist in nature.
Does that mean equations that describe flow of fluids in a wrong way or how we can explain this situation?
Because math is allways 100% correct, 2+2 is always 4, math is apsolute TRUTH..
So,if the math doesn't show correct results then we need to reevaluate what we're doing.. Isnt it?Imagine physicist wrongly state that moment= lever arm + force, using this formula ,results will be allways wrong. But that simple mean, we set wrong equation, they wrongly describe reality,not that math is wrong, so math is always correct.
 
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  • #2
Calculus was not made “mathematically rigorous” until the early 20th century. Were Newton and Leibniz wrong?
 
  • #3
caz said:
Calculus was not made “mathematically rigorous” until the early 20th century. Were Newton and Leibniz wrong?
What do you want to say?
 
  • #4
Most of classical physics was accomplished before mathematicians understood calculus and there was not a large scale reworking when that occurred. One could argue the success of “sloppy calculus” is what drove the efforts to develop rigorous calculus. I would argue that is what is happening with Navier-Stokes.
 
  • #5
caz said:
Most of classical physics was accomplished before mathematicians understood calculus and there was not a large scale reworking when that occurred. One could argue the success of “sloppy calculus” is what drove the efforts to develop rigorous calculus. I would argue that is what is happening with Navier-Stokes.

If someone solve Navier-Stokes problem, than we can describe fluids 100%, even 3D turbulance?
 
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  • #6
Probably not. Even if Navier-Stokes was proven to be solvable, it does not mean it could be solved in a finite amount of time.
 
  • #7
Jurgen M said:
If someone solve Navier-Stokes problem, than we can describe fluids 100%, even 3D turbulance?
No. The Navier-Stokes equations are a model of fluid behavior. They work for physical problems in a certain regime. Case in point, the equations clearly don’t work at the molecular scale, because they assume matter is continuous at every scale.

The mathematical problem of determining the existence and well-behavedness of the solutions to Navier-Stokes is independent from the physical question of how well the equation models fluid behavior at any given scale
 
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  • #8
The Navier Stokes equations are non-linear and can have multiple solutions for the same set of imposed boundary conditions. Only one of the solution is going to be stable, and describe the actual physical situation of interest. If the stable solution to the equations happens to involve turbulence, then there are going to be fluctuations in velocities and stresses, both termporally and spatially. These fluctuations are compatible and consistent with the Navier Stokes equations, although solving for them in detail would be computationally daunting and beyond the capability of current numerical software. So, on a practical basis, obtaining the detailed solution is beyond our present capabilities. However, with turbulence present, the equations can be averaged temporarily, particularly if the behavior is quasi-steady state. But then, information is lost due to the averaging, and approximate methods have been developed to handle such situations. Work is continuing to improve the approximate methods to make them more accurate.
 
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  • #9
Jurgen M said:
Navier-Stokes equations for 3D flow gives us wrong/non existent results, results that don't exist in nature.
this sentence by itself needs accurate and detailed explanation else it is just another quasi-science nonsense
 
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  • #10
Jurgen M said:
Navier-Stokes equations for 3D flow gives us wrong/non existent results, results that don't exist in nature.
You cannot put a pencil on its peak, but it is a possible solution. So? It only means that you cannot set up the initial values precisely enough to obtain a solution in reality. This thread is about modeling physics by equations in general. Navier-Stokes is totally irrelevant to what you said.

This thread is closed because it is hiding a rather general discussion that has nothing to do with a certain model. It is off-topic per topic.
 

1. Why are the Navier-Stokes equations used for 3D flow?

The Navier-Stokes equations are a set of mathematical equations that describe the motion of fluid in three dimensions. They are commonly used in fluid mechanics to study the behavior of fluids, such as air and water, in various situations. These equations are based on fundamental principles of physics and provide a comprehensive understanding of fluid flow.

2. What do you mean by "non-existent results" for 3D flow?

Non-existent results in the context of 3D flow refer to the fact that the Navier-Stokes equations do not always have a solution. This means that for certain complex flow situations, the equations fail to accurately predict the behavior of the fluid. This is due to the highly nonlinear nature of the equations, making it difficult to find solutions for all possible scenarios.

3. Can the Navier-Stokes equations be used for all types of fluids?

No, the Navier-Stokes equations are only applicable to Newtonian fluids, which are fluids that follow a linear relationship between stress and strain. This means that the equations cannot be used for non-Newtonian fluids, such as blood, paint, or shampoo, which exhibit non-linear behavior.

4. Are there any alternative equations that can accurately predict 3D flow?

There are various alternative equations that have been developed to address the limitations of the Navier-Stokes equations. These include the Euler equations, which assume that the fluid is inviscid (has no internal friction), and the Reynolds-averaged Navier-Stokes equations, which use statistical averaging to simplify the equations. However, these equations also have their own limitations and are not applicable in all situations.

5. How do scientists deal with the non-existence of solutions for 3D flow?

There are several approaches that scientists use to deal with the non-existence of solutions for 3D flow. One approach is to simplify the problem by making certain assumptions or approximations, which can make the equations solvable. Another approach is to use computational fluid dynamics (CFD) techniques, which involve solving the equations numerically using powerful computers. Additionally, experimental methods can also be used to study and understand 3D flow situations where the equations fail to provide solutions.

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