Tristan Buckmaster's Statement on the Millennium Prize Problem

Navier-Stokes Equations

Based on research by Tristan Buckmaster, NYU

2024

02

Understanding the Navier-Stokes Challenge

One of mathematics' greatest unsolved problems

01

Fundamental Physics Equations describing the motion of fluid substances like water, air, and oil
02

Practical Applications Essential for weather prediction, aircraft design, ocean currents, and blood flow
03

Mathematical Mystery Despite centuries of use, we cannot prove smooth solutions always exist
04

Clay Institute Prize One of seven Millennium Prize Problems with a $1 million reward

$1,000,000

The Clay Mathematics Institute Prize

Awarded for proving or disproving the existence of smooth solutions to Navier-Stokes equations

05

Progress and challenges in mathematical fluid dynamics

1822

Navier's Contribution

Claude-Louis Navier derives equations from molecular theory

1845

Stokes' Refinement

George Gabriel Stokes provides rigorous formulation

2000

Millennium Prize

Clay Institute designates it a $1M prize problem

2024

Ongoing Research

Buckmaster and others continue investigating singularities

Proving solutions remain well-behaved over time without singularities

Understanding the chaotic behavior of fluid dynamics

Numerical simulations to approximate complex fluid behavior

Investigating whether solutions can break down catastrophically

The Navier-Stokes problem remains one of mathematics' most profound challenges

Source: https://cims.nyu.edu/~tristanb/statement.pdf