Navier–Stokes equations
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The Navier–Stokes equations describe the motion of viscous fluids. This system of partial differential equations was named after Claude-Louis Navier and George Gabriel Stokes, who developed them over
Wire model of flow lines along a Hopf fibration
The Navier–Stokes existence and smoothness problem concerns the mathematical properties of solutions to the Navier–Stokes equations, a system of partial differential equations that describe the motion
Navier–Stokes equations
…conjecture that they have smooth (meaning infinitely differentiable) or bounded solutions in three dimensions has not yet been proven. This is called the Navier–Stokes existence and smoothness problem. The Clay Mathematics Institute has called this one of the seven most important open problems in mathematics and has offered a $1 million prize…
Flow visualization of a turbulent jet, made by laser-induced fluorescence. The jet exhibits a wide range of length scales, an important characteristic of turbulent flows.