Wednesday, May 26

MS45
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(T_n) 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 Geometry and Curvature of New Diffeomorphism Groups and the Averaged Euler Equations

Steve Shkoller, Organizer

Cancelled 10:30-10:55 The Exponential Map on SDiff(T_n) 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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MMD, 4/11/99