where ν ν > 0 is the kinematic viscosity, f ( x , t ) the external volumetric force, ∇ ∇ is the gradient operator and Δ Δ is the Laplacian operator, which is also denoted by ∇ ∇ ⋅ ⋅ ∇ ∇ or ∇ ∇ 2 . Note that this is a vector equation, i.e. it has three scalar equations. Writing down the coordinates of the velocity and the external force