### Non-universal nature of singularities of solutions of the Euler equation

**
Walter Pauls, Observatoire de la Côte d'Azur, Nice, France
**

Using the recently introduced asymptotic interpolation method (http://www.math.u-psud.fr/~vdhoeven/Publs/2006/interpolate.ps.gz)
we have studied numerically the asymptotics of various solutions of
the Euler equation in two and three dimensions. It is found that the
nature of the complex singularities of these solutions depends on the
initial condition. Thus, singularities of the Euler equation are
non-universal which is a most unusual situation in the filed of
nonlinear dynamics. This non-universality is due to the tendency of
the ideal flow to organize itself, at least locally, into structures
with reduced nonlinearity.