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.