Let $u_{?}=rz{e}_{{?}_{?}}(r)-rz{e}_{{?}_{?}}()+u_z{e}_{{?}_{?}}(z)$ and $v_{?}=x^2{e}_{{?}_{?}}(x)-y^2{e}_{{?}_{?}}(y)+v_z{e}_{{?}_{?}}(z)$ represent the velocity fields of two different incompressible fluids $($labeled fluid $1$ and fluid $2,$ respectively$),$ where $$ and $$ are non$-$zero constants. Both fluids are bounded at $z=0$ by a stationary solid boundary. Find the following quantities:

a$.$ The $z-$components of the velocities, $u_z$ and $v_z.$

b$.$ The deviatoric stress tensor, $,$ for each fluid. $($You can use either sign conventions used by the textbook or in class. Just make sure you are consistent.$)$ Use a viscosity of $$ for each fluid.

c$.$ The Laplacian of each of the velocity fields, $gra{d}^{2}u$ and $gra{d}^{2}v$