Let $\Omega$ be a region between two concentric cylinders with radius $R_1$ and $R_2$, where $R_1 < R_2$. A velocity field is given by (in cylindric coorinates $r, \psi, z$): $$v = (- ( A/r + Br) \sin(\psi), (A/r + Br) \cos(\psi), 0)$$
where $ A= \dfrac{R_1^2 R_2^2 (\omega_2 - \omega_1)}{R_2^2 - R_2^2}$, $B= - \dfrac{R_1^2 \omega_1 - R_2^2 \omega_2}{R_2^2 - R_1^2}$.
Why is $v$ a stationary solution of the Euler equations with $\rho = 1$ ?
Edit: And how does the pressure look like ?