Sorry I feel I have not explained myself correctly. Here is a drawing of 
the case:


With Ux may be a profile or a constant.
Initially I had set-up that case with Ux as a Poiseuille flow profile and 
the Top and Bottom as no slip boundary conditions. In that case I got the 
solution I was expecting. Convergence was good and the solution was what I 
had in mind.
Then what I wish to do is set Ux as a constant and apply slip at the top 
and bottom boundary conditions. When I do this is when I am unable to reach 
convergence in my iterative solution, yet I do not understand why because 
the problem should be well posed.
I don't think that leaving my right boundary as a free traction boundary 
condition is problematic since it is by all mean an outlet boundary. This 
worked well for instance in a backward facing step case.
Thank you for your time, sorry for the confusion.
Best regards

On Monday, 19 February 2018 10:50:48 UTC-5, Timo Heister wrote:
> > Does the order in which I apply the nonzero and zero constraints matter? 
> These are two independent objects, so no. 
> > Currently I apply the inlet and then the no-slip in the 
> nonzero_constraints, 
> > thus the bottom and top wall appear after the inlet. Afterward the 
> cylinder 
> > is put in the zero constraints. 
> I don't understand. You need boundary conditions in 
> nonzero_constraints and zero_constraints for all boundaries. The 
> reason for these two sets is that one is used for the initial solve, 
> while the second one is used for the Newton updates. 
> -- 
> Timo Heister 
> http://www.math.clemson.edu/~heister/ 

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