EVIDENCE FOR THE DEVELOPMENT OF SINGULARITIES IN EULER FLOW

This paper is about the problem of determining whether singularities c an develop from analytic initial conditions in the Euler flow of three -dimensional hydrodynamics. The evidence is supplied by previous numer ical simulations. To provide a guide for interpreting this numerical o utput, a theory based on renormalization is outlined here. We conclude that it appears that the numerical results can be satisfactorily expl ained by this theory and that together theory and simulation support t he verdict that singularities exist. Thus a more detailed and rigorous development of the application of the renormalization theory to this system is warranted.