Fluids are awesome.
OK, I might have made it sound easier than it is, but the prize is real! It’s this week’s Millennium Prize Problem, which is part of a series of seven one million dollar prizes to recognize the eventual solution of seven classic mathematical problems that have resisted solution.
To get the million dollars you need to show mathematically that either the Navier-Stokes equations can always be made to give realistic “not blowing up” answers, or that there is a case where they definitely cannot give such a solution. This has to be done for all fluids in three dimensions.
Waves follow our boat as we meander across the lake, and turbulent air currents follow our flight in a modern jet. Mathematicians and physicists believe that an explanation for and the prediction of both the breeze and the turbulence can be found through an understanding of solutions to the Navier-Stokes equations. Although these equations were written down in the 19th Century, our understanding of them remains minimal. The challenge is to make substantial progress toward a mathematical theory which will unlock the secrets hidden in the Navier-Stokes equations.
Good luck to all the math nerds out there.
