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.
Research supported in part by the Air Force Office of Scientific Research under URI grant AFOSR 90-0003, the National Science Foundation through grant NSF-DMS-9005881 and the Alfred P. Sloan Foundation.
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© 1991 Springer-Verlag
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Caflisch, R.E. (1991). Singularity formation for vortex sheets and hyperbolic equations. In: Toscani, G., Boffi, V., Rionero, S. (eds) Mathematical Aspects of Fluid and Plasma Dynamics. Lecture Notes in Mathematics, vol 1460. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0091361
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DOI: https://doi.org/10.1007/BFb0091361
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