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The point vortex model for the Euler equation

1 Faculty of Mathematics, Technische Universit¨at Dresden, 01062 Dresden, Germany
2 Dipartimento di Matematica, Universit`a di Pisa, Largo Bruno Pontecorvo 5, I–56127 Pisa, Italia

Topical Section: Mathematical Analysis in Fluid Dynamics

In this article we describe the system of point vortices, derived by Helmholtz from the Euler equation, and their associated Gibbs measures. We discuss solution concepts and available results for systems of point vortices with deterministic and random circulations, and further generalizations of the point vortex model.
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Keywords point vortex system; Euler equation; Gibbs measures; limit theorems and deviations; generalized SQG

Citation: Carina Geldhauser, Marco Romito. The point vortex model for the Euler equation. AIMS Mathematics, 2019, 4(3): 534-575. doi: 10.3934/math.2019.3.534


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