Wednesday, May 26

Geometric Analysis in Hydrodynamics

10:00 AM-12:00 PM
Room: White Pine

The geometric analysis of geodesic flow on the group of volume-preserving diffeomorphisms, SDiff, answers fundamental questions about the motion of an ideal fluid, such as questions of existence and stability of the solutions to the Euler equations. Recently, great progress has been made in a number of directions: it has been proven that any two fluid configurations can be connected by a generalized flow, the exponential map on SDiff(Tn) has been show to be Fredholm, and new averaged Euler equations have been obtained as geodesics on SDiff with H1 (as opposed to L2) metric. This symposium will explore the connections between these new developments and their consequences for a better understanding of fluid motion.

Organizer: Steve Shkoller
Los Alamos National Laboratory

10:00-10:25 UpdatedGeometry and Curvature of New Diffeomorphism Groups and the Averaged Euler Equations
Steve Shkoller, Organizer
Cancelled 10:30-10:55 The Exponential Map on SDiff(Tn) is Fredholm
Gerard Misiolek, University of Notre Dame
10:30-10:55 The SU(n) Approximation to the 2D Averaged Euler Equations
Sergey Pekarsky, California Institute of Technology
Cancelled 11:00-11:25 Topological Methods in Hydrodynamics
Boris Khesin, University of Toronto, Canada
11:00-11:25 New Pressure Estimates for the 2D Euler Equation    
Peter Topping, MSRI
11:30-11:55 A Nonlinear Analysis of the Averaged Euler Equations
Jerrold E. Marsden, California Institute of Technology

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