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A NOTE ON SINGULARITIES OF THE 3-D EULER EQUATION

S. Tanveer?

Mathematics Department
Ohio State University
Columbus, OH 43210

ABSTRACT

In this paper, we consider analytic initial conditions with finite energy, whose complex spatial continuation is a superposition of a smooth background flow and a singular field. Through explicit calculation in the complex plane, we show that under some assumptions, the solution to the 3-D Euler equation ceases to be analytic in the real domain in finite time.

?This research was partly supported by the National Aeronautics and Space Administration under NASA Contract No. NAS1-19480 while the author was in residence at the Institute for Computer Applications in Science and Engineering (ICASE). Additional support was provided by the Department of Energy (DE- FG02-92ER14270.)

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