We assume here that external forces are described by
and that internal
strains are described by tensor
.
This integral equation corresponds to the applying of Newton's law of
motion\index{momentum} over the elementary fluid volume as shown by
figure figconsp.
Momentum conservation law corresponds to the application of Newton's law of motion to an elementary fluid volume.}
figconsp
Partial differential equation associated to this integral equation is:
Using continuity equation yields to:
Remark:
Momentum conservation equation can be proved taking the first moment of
Vlasov equation. Fluid momentum is then related to repartition
function by the following equality:
Later on, fluid momentum is simply designated by .