The Navier-Stokes equation is a mathematical model that describes the motion of fluids, such as liquids and gases. It is a partial differential equation that relates the pressure, density, temperature, and velocity of the fluid. It also takes into account the effects of viscosity, which is the resistance of the fluid to flow. The equation is named after Claude-Louis Navier and George Gabriel Stokes, who developed it in the 19th century. The Navier-Stokes equation is very useful for studying various phenomena in fluid mechanics, such as weather, ocean currents, aerodynamics, and blood flow.

However, it is also very difficult to solve, and there are still many open questions about its properties and solutions.