Navier-Stokes 方程式について。
Tao: And in fact, in recent years, the consensus has drifted towards the belief that, in fact, for certain very special initial configurations of, say, water, that singularities can form, but people have not yet been able to actually establish this. ...
Fridman: Why is it difficult to prove general things about the set of equations like it not not blowing up?
Tao: Short answer is Maxwell’s Demon. ...
Tao: ... And then you have computers which are made completely out of water. And if you have computers, then maybe you can do robotics, so hydraulics and so forth. And so you could create some machine which is basically a fluid analog, what’s called a von Neumann machine.
... So, if you could build a fluid machine, which yeah, so it’s a fluid robot. And what it would do, its purpose in life, it’s programmed so that it would create a smaller version of itself in some sort of cold state. It wouldn’t start just yet. Once it’s ready, the big robot configuration of water would transfer all its energy into the smaller configuration and then power down. And then they clean itself up, and then what’s left is this newest state which would then turn on and do the same thing, but smaller and faster.
And then the equation has a certain scaling symmetry. Once you do that, it can just keep iterating. So, this, in principle, would create a blowup for the actual Navier-Stokes. And this is what I managed to accomplish for this average Navier-Stokes. So, it provided this sort of roadmap to solve the problem. Now, this is a pipe dream because there are so many things that are missing for this to actually be a reality. ...
ふぁあああ。