Partial differential equations expressing momentum balance for viscous Newtonian fluids, used from aircraft design to blood flow.
Specifications & Metrics
symbol
ρ(Dv/Dt) = −∇p + μ∇²v
Core Principles & Analysis
The equations are named after Claude-Louis Navier and George Gabriel Stokes, who developed them over a few decades.
Proving the existence and smoothness of their solutions is one of seven Millennium Prize Problems, for which the Clay Mathematics Institute offered one-million-dollar prizes in 2000.
They assist in the design of aircraft and cars, the study of blood flow, and the design of power stations.