On the Long Time Behavior of Fluid Flows

This work is devoted to the study of the long time asymptotics of solutions of the Euler equations in a bounded 2-dimensional domain. Experiments and numerical simulations indicate the presence of an attracting set in the space of incompressible velocity fields. In this work this attractor is described, and its attracting property is established in an extended dynamics where the time is replaced by the ‘long time’ taking values in the Alexandroff line. The attracting property in the usual sense remains a conjecture.