# Solution of linear Navier-Stokes equations in a cylindrical coordinates

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Can you advise me please how to solve analytically the linear Navier-Stokes equations in a cylindrical coordinate system. Or share the link please if this solution exists somewhere.

Also there is сontinuity equation

This set of differential equation lacks the initial and boundary conditions for its variables $p$ and $\bf{v}$. As there is no time derivative, this set describes a steady flow within some "geometry" - in a pipe, cone, etc., not necessarily with cylindrical symmetry.

In this task a solid ball rotates around Oy with a constant angular velocity and it is streamlined with velocity U on the Ox by flow of liquid. In cylindric coordinates z is Oy.

Maybe there is some symmetry which reduces equations.

The boundary conditions on this photo:

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