ρ(∂v/∂t + v·∇v) = −∇P + μ∇²v + f combines Newton's laws with viscosity for fluids. v is velocity, P is pressure, μ is viscosity.
Turbulence and mystery
Simple rules produce chaotic turbulence. Whether smooth solutions always exist in 3D is an unsolved millennium prize problem — one of the deepest open questions in mathematics.
Engineering impact
CFD simulations solve Navier-Stokes numerically for aircraft design, weather prediction, blood flow, and Formula 1 aerodynamics.
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