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The L2 exponential map in 2D and 3D hydrodynamics

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No logo availableBanff International Research Station (BIRS) for Mathematical Innovation and Discovery
 Misiolek, Gerard

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The L2 exponential map in 2D and 3D hydrodynamics
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21
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You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
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In the 1960's V. Arnold showed how solutions of the incompressible Euler equations can be viewed as geodesics on the group of diffeomorphisms of the fluid domain equipped with a metric given by fluid's kinetic energy. The study of the exponential map of this metric is of particular interest and I will describe recent results concerning its properties as well as some necessary background.