✎ The Navier-Stokes Equations [The Physics Travel Guide]

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====== The Navier-Stokes Equations ======

The Navier-Stokes equations describe one of the most ubiquitous features of our world: the flow of fluids. They are used to study ocean currents, the turbulence in the wave of an airplane or the flow of blood.

In addition, they are mathematically extremely interesting and there is a [[http://www.claymath.org/millennium-problems|Millennium Prize Problem]] with $1 million reward for the first person who can prove rigorously that solutions exist and answer the question if they are unique.

* [[https://www.quantamagazine.org/what-makes-the-hardest-equations-in-physics-so-difficult-20180116/|What Makes the Hardest Equations in Physics So Difficult?]] (Quanta Magazine)
  * [[https://www.quantamagazine.org/mathematicians-find-wrinkle-in-famed-fluid-equations-20171221/|Mathematicians Find Wrinkle in Famed Fluid Equations]] (Quanta Magazine)
  
<tabbox Student>

<note tip>
In this section things should be explained by analogy and with pictures and, if necessary, some formulas.
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<tabbox Researcher>

<note tip>
The motto in this section is: //the higher the level of abstraction, the better//.
</note>

--> Example1#

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--> Example2:#

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<tabbox FAQ> 
--> What makes the Navier-Stokes equations so difficult?#

See the discussion [[https://www.physicsforums.com/threads/what-makes-the-navier-stokes-equation-so-difficult.937175/|here]].

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<tabbox History>

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