Navier-Stokes

1.

Навье Стокс
Existence and smoothness
Nikita Belousov

2.

Glossary
Fluid
a liquid or gas
Viscosity
internal friction
Smooth solution
well-behaved derivatives
Singularity
breakdown of smoothness

3.

Presentation Plan
01
History and the question
02
The Millennium list
03
Attempts and current status

4.

From Physics to Equations
19th century
Claude-Louis Navier
George Gabriel Stokes

5.

The Mathematical Question
Smooth forever?
Or breakdown in finite time?

6.

A Millennium Prize Problem
2000
Paris, 24 May
$1 million for a solution

7.

How Researchers Approached It
1934
Leray: weak solutions
Special cases and simulations

8.

Current Status
A claimed solution
8 September 2026: OpenAI
24 September: Clay lists “Active”

9.

Questions
01
When did it become a Millennium Prize Problem?
02
Has it been solved yet?
03
Who formulated the problem?