>> Is it possible to extend your code to time dependent Navier-Stokes
>> equations?

Certainly, but one could also start from one of the Stokes examples. I
don't know if starting from step-57 is the best approach for you,
because one would typically use a stable linearized time stepping
method instead of solving the nonlinear system using Newton's method
in each timestep. An example would be linearized BDF2 for example.

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