Loading...
research article
On a Lagrangian Formulation of the Incompressible Euler Equation
In this paper we show that the incompressible Euler equation on the Sobolev space H-s(R-n), s> n/2+1, can be expressed in Lagrangian coordinates as a geodesic equation on an infinite dimensional manifold. Moreover the Christoffel map describing the geodesic equation is real analytic. The dynamics in Lagrangian coordinates is described on the group of volume preserving diffeomorphisms, which is an analytic submanifold of the whole diffeomorphism group. Furthermore it is shown that a Sobolev class vector field integrates to a curve on the diffeomorphism group.
Type
research article
Web of Science ID
WOS:000390012400005
Authors
Publication date
2016
Publisher
Published in
Volume
29
Issue
4
Start page
320
End page
359
Peer reviewed
REVIEWED
EPFL units
Available on Infoscience
January 24, 2017
Use this identifier to reference this record