  The search of finite-time singularity solutions of Euler equations is
considered for the case of an incompressible and inviscid fluid. Under the
assumption that a finite-time blow-up solution may be spatially anisotropic as
time goes by such that the flow contracts more rapidly into one direction than
into the other, it can be shown that the dynamics of an axially symmetric flow
with swirl may be approximated to a simpler hyperbolic system. By using the
method of characteristics, it can be shown that generically the velocity flow
exhibits multi-valued solutions appearing on a rim at a finite distance from
the axis of rotation which displays a singular behavior in the radial
derivatives of velocities. Moreover, the general solution shows a genuine
blow-up which is also discussed. This singularity is generic for a vast number
of smooth finite-energy initial conditions and is characterized by a local
singular behavior of velocity gradients and accelerations.
