  A partial differential equation has usually a regular solution at the initial
time if the initial condition is smooth in space, fulfills the governing
equations and is compatible with the boundary condition. In the case of
Navier-Stokes equation, the initial velocity field must also be
divergence--free. It is common belief that the initial condition is compatible
with the boundary condition if the initial condition fulfills the boundary
condition but this is not sufficient. Such a field does not necessarily fulfill
the full compatibility condition of the Navier-Stokes equation. If the
condition is violated, the solution is not regular at the initial time. This
issue has been known for a while but not in the full breadth of the fluid
dynamics community. In this paper, a practical calculation method is presented
for checking the compatibility condition. Furthermore, a smooth initial
condition is presented in a periodic channel flow that violates the condition
and has no spatially smooth solution at initial time. The calculations were
were performed in an analytical framework. The results for a channel
configuration show that in the absence of wall--normal velocity the condition
is always fulfilled and the problem has a regular solution. If the wall--normal
velocity component is non--zero, the condition is usually not fulfilled but
with optimization methods counter-examples can be generated. The generation
procedure of such a field is useful to provide correct initial conditions for
sensitive time-dependent numerical simulations. The presented methods can
provide insight about the applicability of the chosen initial conditions.
