Derivation of the Navier–Stokes equations

Why can't we always predict fluid motion in real life?

Imagine trying to predict how a cup of coffee will spill when you tilt it too fast.

The difficulty is like trying to understand every tiny movement of coffee particles as they swirl and mix, which is what the Navier-Stokes equations aim to do. They are mathematical equations that describe how fluids like coffee flow.

Example

If you tilt a cup of coffee at a certain angle, you can predict where it will spill, but only if you know the coffee's speed and direction at every point.

Remember this

The Navier-Stokes existence and smoothness problem is about proving whether these equations can always predict fluid motion accurately for every possible situation.

Text adapted from Wikipedia, licensed under CC BY-SA 4.0.

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