What is generic approach to solving this system?
$ \rho\left({\partial v_i \over\partial t}+v_k{\partial v_i \over \partial x_k} \right) = - {\partial p \over\partial x_i} + {\partial \over\partial x_k}\left\{ \mu \left({\partial v_i \over\partial x_k}+{\partial v_k \over\partial x_i} - {2\over 3}\delta_{i,k}{\partial v_l \over\partial x_l}\right) \right\}+{\partial \over\partial x_k}\left( \zeta {\partial v_l \over\partial x_l}\delta_{i,k}\right) $
$\vec{v}|_{\partial \Omega} = 0, \quad \vec{v}|_{t=0} = \vec{v}_{0}$
I finished a course in differential math and PDE, but I can't even say what is the kind of the task.
The task is to be solved numerically.
PS: or can anybody say something about last two formulas? What is "\partial \Omega" ($\partial \Omega$) usually means?