Steve Shkoller

collaborators

2 papers

math.DG1999

Reduction in principal fiber bundles: covariant Euler-Poincare equations

Marco Castrillon Lopez, Tudor S. Ratiu, Steve Shkoller

Let $π : P \to M^{n}$ be a principal G-bundle, and let $L : J^{1} P \to Λ^{n} (M)$ be a G-invariant Lagrangian density. We obtain the Euler-Poincare equations for the reduced Lagran…

math.AP1999

The geometry and analysis of the averaged Euler equations and a new diffeomorphism group

J. E. Marsden, T. S. Ratiu, S. Shkoller

We present a geometric analysis of the incompressible averaged Euler equations for an ideal inviscid fluid. We show that solutions of these equations are geodesics on the volume-pr…