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On a Lagrangian Formulation of the Incompressible Euler Equation

On a Lagrangian Formulation of the Incompressible Euler Equation

Year:    2016

Author:    Hasan Inci

Journal of Partial Differential Equations, Vol. 29 (2016), Iss. 4 : pp. 320–359

Abstract

In this paper we show that the incompressible Euler equation on the Sobolev space Hs(Rn),sn2+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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jpde.v29.n4.5

Journal of Partial Differential Equations, Vol. 29 (2016), Iss. 4 : pp. 320–359

Published online:    2016-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    40

Keywords:    Euler equation

Author Details

Hasan Inci

  1. On the local well‐posedness of the 1D Green–Naghdi system on Sobolev spaces

    İnci, Hasan

    Mathematische Nachrichten, Vol. 297 (2024), Iss. 1 P.52

    https://doi.org/10.1002/mana.202200256 [Citations: 0]
  2. On the local well–posedness of the two component b-family of equations

    Inci, Hasan

    Monatshefte für Mathematik, Vol. 197 (2022), Iss. 3 P.479

    https://doi.org/10.1007/s00605-021-01602-z [Citations: 3]