Abstract
We prove, via a pathwise analysis, an existence result for stochastic differential equations with singular coefficients that govern stochastic vortex systems. The techniques are self-contained and rely on careful estimates on the displacements of particles, obtained by recursively identifying “vortex clusters“ whose mutual interactions can be controlled. This provides a non trivial extension of techniques of Marchioro and Pulvirenti(7) for deterministic motion of vortices.
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AMS subject classification: 60H10, 60K35, 76B47
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Fontbona, J., Martinez, M. Paths Clustering and an Existence Result for Stochastic Vortex Systems. J Stat Phys 128, 699–719 (2007). https://doi.org/10.1007/s10955-007-9339-4
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DOI: https://doi.org/10.1007/s10955-007-9339-4