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The finite time singularity solution for a single vortex field in
both viscous and non viscous fluids is discussed. The Leray
transformation, which gives self similar solutions for (local)
inner region of incompressible fluids, is generalized to a
dynamical time dependent case. A new generalized time \emph{T} is
introduced to modify the Leray equation. Two important examples
are generalized to produce both decreasing and constant areas of
singularity instead of an exact line of singularity in the self-similar solutions. This is done by assuming a "line source" of the matter in the core of the singularity.
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