 Navier-Stokes equation

The Navier-Stokes equation is momentum conservation for a fluid with a specified viscous constitutive equation. In the incompressible Newtonian fluid model below, $\rho$ is constant mass density, $\mu$ is constant dynamic viscosity, $p$ is pressure, and $f$ is external force per unit mass.

For an incompressible Newtonian fluid of constant density and viscosity,

The left side is mass density times the material acceleration. The pressure gradient, viscous momentum transport and external forcing supply the right side. The condition $\nabla \cdot u=0$ constrains the velocity field; suitable initial and boundary conditions are still needed to determine a flow. ^[ref]