# Introduction to Mathematical Physics/Continuous approximation/Momentum conservation

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.

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 .