= Solution
The rigid-rotation <velocity field> is $\mathbf v=(-\Omega y,\Omega x,0)$, with spatially uniform $\Omega(t)$. Its divergence is zero, since $\partial_x(-\Omega y)=\partial_y(\Omega x)=0$. It therefore satisfies the incompressible <continuity equation>. On the cylindrical wall, $\mathbf v\cdot(x,y,0)=0$, so it has zero normal <velocity>; on either end cap its vertical component is zero. These are the impermeability <boundary conditions> for an <inviscid flow>. Tangential slip is permitted; a no-slip condition is not part of this inviscid model.
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