I find two versions of the Cauchy momentum equation ([1][1], [2][2]):
$$
\rho \frac{D\vec{v}}{Dt}=\rho\vec{g} - \nabla{p} + \mu\nabla^2\vec{v}
$$
$$
\rho \frac{D\vec{v}}{Dt}=\rho\vec{g} - \nabla{p} + \nabla \cdot \bf\tau
$$
and I'm tempted to conclude that $\mu\nabla^2\vec{v} = \nabla \cdot \bf\tau$

However, when I expand and compare terms on both sides of the equation they look widely different. **Does this equality actually hold? What should the expanded terms look like?**

  [1]: https://community.dur.ac.uk/suzanne.fielding/teaching/BLT/sec1.pdf
  [2]: https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_equations#General_continuum_equations