Eigenvalue solution for the self similar Birkhoff—Rott equation.

  • Sergio Rica
Conference paper
Part of the Nonlinear Phenomena and Complex Systems book series (NOPH, volume 9)


This paper adress to the equation \( (v - \omega {\partial _\omega })\bar \varphi (\omega ) = \frac{1}{{2\pi i}}P\int_0^\infty {\frac{{d\omega '}}{{\bar \varphi (\omega ) - \bar \varphi (\omega ')}}} \), in particular I will discuss solutions depending on the value of v. This equation is usefull for the study of the selfsimilar rolling-up of a semi-infinite vortex sheet.


Vortex Sheet Finite Time Singularity Maclaurin Formula Eigenvalue Solution Dilatation Invariance 
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Copyright information

© Springer Science+Business Media Dordrecht 2004

Authors and Affiliations

  • Sergio Rica
    • 1
    • 2
  1. 1.Departamento de Física, FCFMUniversidad de ChileSantiagoChile
  2. 2.Laboratoire de Physique Statistique de l’Ecole Normale SupérieureParis Cedex 05France

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