Navier–Stokes equations

Summary

The Navier–Stokes equations describe the motion of a viscous fluid, such as water or air. They are Newton's second law for each small parcel of fluid, with forces from pressure, internal friction and external sources. In the incompressible case they form a nonlinear system for the velocity field and the pressure. Whether smooth solutions in three dimensions stay smooth for all time is one of the Millennium Prize Problems.