The point vortex model for the Euler equation

Abstract

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.

Keywords

• point vortex system
• Euler equation
• Gibbs measures
• limit theorems and deviations
• generalized SQG