I don’t want to judge, but I’m gonna guess that you haven’t. Basically, the Navier-Stokes equations is a bunch of mega complicated maths that describes fluid dynamics (how fluids flow). They’re so complicated in fact, that we don’t even know what the full set looks like yet. As such, they’ve become one of the Millennium Prize Problems; seven maths problems that are so impenetrable, you win $1,000,000 if you can solve just one!!
But why should you care about these horrendous maths equations? Well you shouldn’t really. It’s what they describe that is the interesting bit.
Imagine a drainpipe. Nice and smooth bit of tubing. If you prop one end of the drainpipe up on a few bricks, you can poor water down it. But now watch carefully; no matter how smoothly and consistently you pour the water in at the top, it will always form little crests and troughs as it goes down. It will never have a nice smooth surface the whole way. Pretty odd right?
Now most observations we make in the world can be explained pretty well by some king of mathematical model. For example the planets going around the sun or the spread of bacteria in a Petri dish can be nicely understood with equations. However it turns out that this spontaneous ‘jumping up’ of the water in a tube is ridiculously difficult to explain with maths. To be honest, the closest we can get is putting the relevant information into a hench super-computer to do the figuring out for us. But even this turns out to be a bit wrong.
So this is why there is such a big prize for the man or woman that can rigorous mathematical model to describe how fluid flows. So you never know- if your bank account is looking a little slim and you fancy a challenge…