Reading a book, I found the following Navier-Stokes equations:
$ \rho \Big( \frac{\partial \vec{u}}{\partial t} + \vec{u} \cdot \nabla \vec{u}\Big) + \nabla p = \nabla \cdot {\sigma} + \vec{f}, $
$ \nabla \cdot \vec{u} =0. $
Here the viscous stress tensor is given by ${\sigma} : = \mu ( \nabla \vec{u} + (\nabla u)^{T})$. Then, I think $\sigma$ should a matrix. But, I'm not sure how $\nabla \cdot \vec{\sigma}$ looks like when $\vec{u} = (u_{1}, u_{2}, u_{3})$. Did I understand something wrong? Or, could you help me out?