The Navier-Stokes equations for the flow of a viscous incompressible fluid with flow velocity u state

Here ρ‎ denotes the (constant) density, p denotes pressure, ν‎ denotes the constant viscosity, g denotes acceleration due to gravity, and D/Dt is the convective derivative. Note that if ν‎ =  0, then the Navier-Stokes equations become Euler’s equations.