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.


Published in:
Journal Of Partial Differential Equations, 29, 4, 320-359
Year:
2016
Publisher:
Wanchai, Global Science Press
ISSN:
2079-732X
Keywords:
Laboratories:




 Record created 2017-01-24, last modified 2018-03-13


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