Navier–Stokes Equations

A system of coupled nonlinear partial differential equations expressing conservation of mass (continuity) and linear momentum for a viscous, Newtonian continuum: ρ(∂u/∂t + u·∇u) = −∇p + μ∇²u + ρf together with ∇·u = 0 for incompressible flow, where u is velocity, ρ density, p pressure, μ dynamic viscosity and f body force per unit mass.

A set of nonlinear partial differential equations expressing conservation of momentum (and mass) for a viscous Newtonian continuum fluid. For incompressible flow: ρ(∂u/∂t + u·∇u) = −∇p + μ ∇^2 u + ρ f, together with ∇·u = 0. Here ρ is density, u velocity field, p pressure, μ dynamic viscosity and f body forces per mass.