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Paper IPM / Physic / 7220  


Abstract:  
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 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 selfsimilar solutions. This is done by assuming a "line source" of the matter in the core of the singularity.
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