Non-viscous incompressible Fluid between two coaxial cylinder

Consider a non-viscous incompressible fluid lies between two coaxial cylinders. The domain occupied by the fluid is defined as $$0, $$A. The coaxial cylinders slowly rotate arround their $$z$$-axis with angular velocity $$\Omega$$ Suppose that the height of this fluid at rest is $$H$$ and the density $$\rho$$ of the fluid is constant.

We use cylinderical coordinates $$\vec{V}=V_r \hat{e_r} +V_{\theta} \hat{e_{\theta}}+V_{z} \hat{e_z}.$$

My Question is about the boundary conditions.

I have on the outer cylinder $$V_r =0$$. I have read a paper dealing with the same problem one cylinder and the boundary conditions is $$V_r = 0$$ on the wall and $$V_z =0$$ on the bottom. Is there any conditions must be taken on the inner cylinder?

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• How can the fluid start rotating without viscosity? And, which interactions between the fluid and other parts of the system are not neglected, as these will provide us with the boundary conditions? – acarturk May 21 '19 at 1:31