It is useful to describe the equation for momentum
.
Eulerian derivative of momentum density
is rewritten as

(A.12) |

where we used equations (A.7) and (A.11). In the Cartesian cordinate , this becomes

(A.13) |

(A.14) |

where represents the Kronecker's delta as for and for .

If there is no external force, rhs of equation (A.15)
is equal to zero.
If the momentum density
were to obey the continuity equation,
equation (A.15) would be

Kohji Tomisaka 2012-10-03