Navier-Stokes is actually Newton’s second law of motion in disguise. The left-hand side is the acceleration of a small fluid region, and the right-hand side is the forces that act on it: pressure, stress, and internal body forces. This formula provides a really accurate way to calculate how fluids move, and it is a key feature of innumerable scientific and technological problems. Navier-Stokes led us to modern passenger jets, fast and quiet submarines, Formula-1 racing cars that stay on the track at high speeds, and medical advances on blood flow in veins and arteries.
Mathematics is much more than routine calculations. That's what David Darling aims to show in this series of mathematics videos.