  Classical vorticity solution branches of the three dimensional incompressible
Euler equation are constructed where a velocity component can blow up at some
point after finite time for regular data in H2. Furthermore, vorticity can blow
up after finite time for data in H2, and there are classical solution branches
with regular data which develop weak singularities at some point of space time
after finite time. The construction of these time-local solution branches is by
viscosity limits of viscosity extensions of time-reversed Euler-type equations.
The short time (weak) singularities are then initial values of local solution
branches of the time-reversed Euler type equations, which are constructed via
(not time-reversible) viscosity extensions. These solutions of the 3-D Euler
equation have a straightforward interpretation as solution of incompressible
Navier Stokes equation with time dependent force terms with restricted
regularity or blow up of a velocity component at some point, as the
time-dependent force term can be chosen such that it cancels the viscosity term
of the incompressible Navier Stokes equation.
