The two dimensional Euler equation is globally well-posed. The long time behavior of solutions are however very hard to understand. Numerical and physical experiments show that vortices form naturally in 2D Euler flows and could become a dominant feature of the long time dynamics. Point vortex solutions are one of the most physically relevant 2D vortices, which model the situation when vorticity concentrates sharply near a point.

 In this talk, we will discuss our recent result establishing the nonlinear asymptotic stability of point vortex solutions to the 2D Euler equation, which appears to be the first result describing the precise dynamics of 2D Euler equation with generic initial data in the plane. The talk is based on joint work with A. Ionescu.