Concentrated Euler flows and point vortex model

Abstract

This paper is an improvement of previous results on concentrated Euler flows and their connection with the point vortex model. Precisely, we study the time evolution of an incompressible two dimensional Euler fluid when the initial vorticity is concentrated in N disjoint regions of diameter ɛ. We show that the evolved vorticity is concentrated in N regions of diameter d, d ≤ b ɛ^α (b independent of ɛ) for any α < 1/2. The connection is obtained as ɛ→0.

Keywords

• euler flow
• concentrated vorticity
• point vortex model