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

Weak singularities of 3-D Euler equations and restricted regularity of Navier Stokes equation solutions with time dependent force terms