Navier-Stokes Equation
1. This is the
equation which governs the flow of fluids such as water and air. However, there
is no proof for the most basic questions one can ask: do solutions exist, and
are they unique? Why ask for a proof? Because a proof gives not only certitude,
but also understanding.
2.
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.
3.
Existence & smoothness of the Navier-Stokes
equation, by Charles L. Fefferman