Navier–Stokes existence and smoothness

The Navier–Stokes existence and smoothness problem is a major unsolved problem in mathematics that deals with the mathematical framework of fluid dynamics. Specifically, it pertains to the behavior of solutions to the Navier–Stokes equations, which describe the motion of viscous fluid substances. The Navier–Stokes equations are a set of nonlinear partial differential equations that describe how the velocity field of a fluid evolves over time under various forces.