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We show that, for two-dimensional space-periodic incompressible flow, thesolution can be evaluated numerically in Lagrangian coordinates with the sameaccuracy achieved in standard Eulerian spectral methods. This allows thedetermination of complex-space Lagrangian singularities. Lagrangiansingularities are found to be closer to the real domain than Euleriansingularities and seem to correspond to fluid particles which escape to(complex) infinity by the current time. Various mathematical conjecturesregarding Eulerian/Lagrangian singularities are presented.

Complex-space singularities of 2D Euler flow in Lagrangian coordinates