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Title:
Asymptotic geometry and asymptotic dynamics of 2-d ideal incompressible fluid
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Abstract:
Consider the flow of the ideal incompressible fluid in a bounded 2-dimensional domain M. It is described by the velocity field u(x,t). How does this field behave as the time t goes to infinity? In this talk I concentrate on the geometrical side of this problem. The configuration space of the fluid is the group D of volume preserving diffeomorphisms with the energy metric. As a metric space, D has infinite diameter (Eliashberg & Ratiu); therefore it makes sense to consider its asymptotic space (or asymptotic cone) at infinity (Gromov). Its structure turns out to be quite rich, and provides valuable clues on the actual long-time behavior of the flows.
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