3D Cartesian Gov. Eq. confusion
 

Hi, I am a new user and trying to derive the equation for a 3D cartesian - momentum conservation equation in the x direction. I arrived to the equation below.

dñu/t + ñ(u dU/dx + v dU/dy + w dU/dz) = m(d2u/dx2 + 2du/dy2 + d2u/dz2) - dP/dx + Source

m = viscosity u,v,w = x, y, z components of velocity. U = velocity vector.

Is the above equation correct? How can i derive the equation as presented in the document below? http://ej.iop.org/links/q28/2JJzEqNT...DTg/d22406.pdf

thanks and regards kay