Navier–Stokes equations
Statement
The Navier–Stokes equations describe the motion of viscous fluid substances. They govern the motion of Newtonian fluids—from air and water to blood—and are fundamental to fluid dynamics in engineering, meteorology, and physiology.
Formula
Momentum balance: mass × acceleration = pressure gradient + viscosity + body forces
Equation
ρ(∂v/∂t + v·∇v) = -∇p + μ∇²v + f
Source
Navier, Mémoire sur les lois du mouvement des fluides, 1822. Stokes, On the theories of the internal friction of fluids in motion, 1845.
Domains
mathematics, physics