Abstract
We consider the motion ofN vortices in bounded domains in IR2. We prove that the set of initial positions which lead to a collapse of two or more vortices has Lebesgue measure zero. We extend this result to the stochastic motion of the vortices, where the stochasticity comes from a Wiener-noise term, which is added to the deterministic equation of motion.
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Communicated by J. Lebowitz
On leave of the Fachbereich Mathematik, RUB, 4630 Bochum, Federal Republic of Germany. Supported by a DFG-fellowship
Partially supported by Italian CNR
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Dürr, D., Pulvirenti, M. On the vortex flow in bounded domains. Commun.Math. Phys. 85, 265–273 (1982). https://doi.org/10.1007/BF01254459
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DOI: https://doi.org/10.1007/BF01254459