The Navier-Stokes existence and smoothness problem is a fundamental unsolved question in mathematical physics, asking whether solutions to the Navier-Stokes equations, which describe the motion of fluid substances, always exist and remain smooth in three dimensions. Solving this problem is one of the seven Millennium Prize Problems, with a reward of one million dollars for a correct solution or counterexample.

Navier-Stokes Existence And Smoothness

Navier-Stokes existence and smoothness problem

fundamental unsolved question

Mathematical physics is a discipline that applies rigorous mathematical methods to solve problems in physics and develop new physical theories. It bridges the gap between mathematics and physics by providing a framework for formulating and analyzing the mathematical structures underlying physical phenomena.

mathematical physics

solutions to the Navier-Stokes equations

motion of fluid substances

Smooth solutions

three dimensions

Solving this problem

The Millennium Prize Problems are a set of seven unsolved mathematical problems, each with a prize of one million dollars for a correct solution, established by the Clay Mathematics Institute in 2000 to celebrate the turn of the millennium and to stimulate interest in important mathematical questions. As of now, only one of the problems, the Poincaré Conjecture, has been solved, highlighting the complexity and significance of these challenges in the field of mathematics.

Millennium Prize Problems

reward of one million dollars

correct solution

A counterexample is a specific case that disproves a general statement or proposition by demonstrating an exception. It is a powerful tool in logic and mathematics for testing the validity of universal claims and refining theories.

CUSTOMIZE YOUR LEARNING

CUSTOMIZE YOUR LEARNING

Relevant Degrees