Cauchy momentum equation
= Cauchy momentum equation
{c}
The Cauchy momentum equation balances material acceleration against stress divergence and body force:
$$
\rho\frac{D\mathbf u}{Dt}=\nabla\mathbin\cdot\boldsymbol\sigma+\rho\mathbf b.
$$
For an inertialess flow, the left-hand side is neglected.