Terence Tao

Just the aggregate behavior is important.

But if you want to model a fluid, like the weather, you can't just say in Los Angeles, the temperature is this, the wind speed is this.

For supercritical equations, the finite scale information is really important.

Can you describe this idea?

Right, yeah.

So this came out of this work of constructing this average equation that blew up.

So one...

As part of how I had to do this, there's sort of this naive way to do it.

You just keep pushing.

Every time you get energy at one scale, you push it immediately to the next scale as fast as possible.

This is sort of the naive way to force blow up.

It turns out in five and higher dimensions, this works.

But in three dimensions, there was this funny phenomenon that I discovered, that if you keep...

change the laws of physics, you just always keep trying to push the energy into smaller and smaller scales.

What happens is that the energy starts getting spread out into many scales at once.

So you have energy at one scale, you're pushing it into the next scale, and then

as soon as it enters that scale, you also push it to the next scale, but there's still some energy left over from the previous scale.

You're trying to do everything at once.

And this spreads out the energy too much.

And then it turns out that it makes it vulnerable for viscosity to come in and actually just damp out everything.