Navier-Stokes equations

The Navier–Stokes equations are a system of nonlinear partial differential equations that describe the motion of viscous fluids, expressing conservation of mass and momentum while accounting for quantities such as velocity, pressure, density, and viscosity. They underpin mathematical and computational modeling of fluid flow; a famous unresolved question asks whether smooth, physically meaningful solutions in three dimensions can develop singularities (finite-time blow-up), which is why claims that AI has “solved Navier–Stokes” refer to a major mathematical or computational result rather than to a namesake.