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Paper   IPM / Physic / 7220
School of Physics
  Title:   The Generalized Leray Transformation for Finite Time Singular Vortices in Fluids
  Author(s): 
1.  H. Eshraghi
2.  Y. Abedini
  Status:   In Proceedings
  Proceeding: Proceedings of the Fifth International Conference on Symmetry in Non Linear Mathematical Physics, Proceedings of Institute of Mathematics of NAS of Ukraine,2004, p.715-721
  Vol.:  50, Part 2
  Year:  2004
  Pages:   715-721
  Supported by:  IPM
  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 self-similar solutions. This is done by assuming a "line source" of the matter in the core of the singularity.

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