Navier-Stokes equations

The Navier-Stokes equation is an equation in fluid mechanics that states:

$\text{[math]}$

where $\text{[math]}$ is the pressure difference (expressed as the partial derivative of pressure in each dimension), $\text{[math]}$ is the total derivative of velocity, $\text{[math]}$ is the kinematic viscosity of the fluid, $\text{[math]}$ is the density of the fluid, and $\text{[math]}$ is the gravitational acceleration.^[1]