Abstract
Singularities are expected to occur in a variety of inviscid incompressible flows, the simplest being on a vortex sheet just preceding roll-up of the sheet. We present a new approach to the vortex sheet problem, in which the Birkhoff-Rott equation is approximated by a system of first order non-linear pde's. The system is solved in an analytic function setting, and singularities occur as branch points for the solution. In this paper, the general method is applied to Burger's equation and to the short time existence problem for a 2x2 system with initial singularities.KeywordsRiemann SurfaceBranch PointBurger EquationPoint VortexVortex SheetThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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