How to pronounce “navier” in English

So the Navier-Stokes equations that govern a fluid flow or incompressible fluids like water.

So in Navier-Stokes, there's the dissipation force coming from viscosity, and it's very well understood, it's linear, it calms things down.

And the fluid Navier-Stokes is a continuous equation.

- Can you speak to the Navier-Stokes?

There's something called the Compressible Navier-Stokes, which governs things like air.

- If we can just linger on the Navier-Stokes equations a little bit.

And that's the analogous situation with Navier-Stokes.

There's a famous unsolved problem called the Navier-Stokes regularity problem.

So this Clay prize problem concerns what's called the Incompressible Navier-Stokes, which governs things like water.

A lot of it is actually just trying to solve the Navier-Stokes equations as best they can.

and you can keep everything under control for not just the Navier-Stokes, but for many, many types of equations like this.

But if I could average the equations of motion of Navier-Stokes, basically, if I could turn off certain types of ways in which water interacts and only keep the ones that I want.

So there are these two competing terms in the Navier-Stokes equation, the dissipation term and the transport term.

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.

There are other groups who are now pursuing ways to make Navier-Stokes blowup, which are nowhere near as ridiculously complicated as this.

- There is a real leap of genius here to go from Navier-Stokes to this Turing machine.

Okay, so getting back to Navier-Stokes, a fluid has a certain amount of energy, and because the fluid is in motion, the energy gets transported around.

So what that means is that if you wanted to prove global regularity for Navier-Stokes, for the actual equation, you must use some feature of the true equation,

And in two dimensions, the Navier-Stokes equations is what's called critical.

And so that is part of what inspired me to propose the same thing with Navier-Stokes, which is a much, as I said,

So the Kakeya conjecture is not directly, directly related to the Navier-Stokes problem, but understanding it would help us understand some aspects

of things like wave concentration, which would indirectly probably help us understand the Navier-Stokes problem better.

They're going to be attacks on the most fundamental and important questions of the day, whether it's the Riemann hypothesis, Navier-Stokes or P versus NP,

I mean, fluid dynamics, Navier-Stokes equations, these are traditionally thought of as very, very difficult intractable problems to do on classical systems.

I mean, fluid dynamics, Navier-Stokes equations, these are traditionally thought of as very, very difficult intractable kind of problems

In 2016, you published a paper, "Finite Time Blowup for an Averaged Three-Dimensional Navier-Stokes Equation."

And so in the past, there have been many attempts to try to obtain what's called global regularity for Navier-Stokes, which is opposite of finite-time blowup,