Mathematicians Want To Make Fluid Equations Glitch Out

So this story has some physics energy to it, which is what got me into it as a physics reporter, but really, as you mentioned, it's a pure math story.

So the physics energy comes from the fact that we have these incredible equations, the Navier-Stokes equations, and they're just as rich, and they're just as beautiful as the equations that describe quantum mechanics or the equations that describe space time and general relativity, but they describe fluids, so whirlpools, water flowing, all that good stuff.

Mm-hmm.

So that's the physics side.

Now, these equations, being equations, are also pure math objects, and partially because they're so famous and so interesting, mathematicians are also just motivated out of pure curiosity to understand them at the mathematical level.

So the big idea here is mathematicians want to answer a simple yes or no question about these mathematical objects.

That is, do all of their solutions make sense? Are they physical at all places, at all times? Do they describe liquids that always behave in a logical way or not?

The Navier-Stokes equations are very successful in general with describing real phenomenon in fluids, but what we're looking at here is probing the limits of where they might actually break down and not be able to describe something in the real world.

Yeah, exactly.

Got it.

Okay, so when you're describing the Navier-Stokes equations to a non-physicist, to a non-mathematician, how do you typically describe them?

So they are the fluid version of another famous and perhaps more familiar equation, Newton's second law of motion.

That's F equals MA, force equals mass times acceleration.

F equals MA tells you about what an object is doing in response to a certain force, and it has lots of solutions.

It describes a book or a laptop sitting on a table and not doing anything.

It describes a rock falling off of a building.

Yeah.

It describes a cannonball's parabolic trajectory through space.

Mm-hmm.

Right? So these are all different solutions to F equals MA.

And the Navier-Stokes equations are like that, but for fluid.

They're actually very similar, force applied to different points and, of the fluid and what happens as a result.

And so the different solutions to the Navier-Stokes equations are similar.

It could be water in a fish tank just sitting there doing nothing.

It could be a whirlpool, water flowing down a river.