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Vortices and localization in Euler flows

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Abstract

We study the time evolution of a non-viscous incompressible two-dimensional fluid when the initial vorticity is concentrated inN small disjoint regions of diameter ε. We prove that the time evolved vorticity is also concentrated inN regions of diameterd, vanishing as ε→0. As a consequence we give a rigorous proof of the validity of the point vortex system. The same problem is examined in the context of the vortex-wave system.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università “La Sapienza”, Piazzale A. Moro 2, I-00185, Roma, Italy

    Carlo Marchioro & Mario Pulvirenti

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  1. Carlo Marchioro
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  2. Mario Pulvirenti
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Communicated by J.L. Lebowitz

Research partially supported by MURST, (Ministero dell'Università e della Ricerca Scientifica e Tecnologica), CNR (Consiglio Nazionale delle Ricerche-Gruppo Nazionale per la Fisica Matematica) and CNR contract n.92.00544.01

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Marchioro, C., Pulvirenti, M. Vortices and localization in Euler flows. Commun.Math. Phys. 154, 49–61 (1993). https://doi.org/10.1007/BF02096831

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  • DOI: https://doi.org/10.1007/BF02096831

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