Analysis Seminar

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From Point Vortices to 2D Incompressible Euler in the Mean-Field Limit

Speaker: Matthew Rosenzweig, MIT

Location: TBA

Date: Thursday, November 12, 2020, 11 a.m.

Synopsis:

In this talk, we consider the classical Helmholtz-Kirchoff point vortex system in the mean-field regime where the magnitudes of the vortex circulations are inversely proportional to the number of vortices. When the number of vortices is very large, the evolution of this system is approximately described by the vorticity formulation of the two-dimensional incompressible Euler equation. We will present a result on this approximation problem when the limiting vorticity is only in $L^\infty$, a scaling-critical function space for the well-posedness of the equation. Time permitting, we will discuss the generalization to higher dimensions and current work on the mean-field approximation when multiplicative noise is added to the dynamics.

Notes:

This is an online talk via Zoom.