The geometry of a vorticity model equation

verfasst von

Joachim Escher, Boris Kolev, Marcus Wunsch

Abstract

We show that the modified Constantin-Lax-Majda equation modeling vortex and quasi-geostrophic dynamics [27] can be recast as the geodesic flow on the subgroup Diff^∞₁(S) of orientation-preserving diffeomorphisms φ ∈ Diff^∞(S) such that Φ(1) = 1 equipped with the right-invariant metric induced by the homogeneous Sobolev norm Ḣ_1/2. On the extended group of diffeomorphisms of Sobolev class H^k with k ≥ 2, this induces a weak Riemannian structure. We establish that the geodesic spray is smooth and we obtain local existence and uniqueness of the geodesics.

Organisationseinheit(en)

Institut für Angewandte Mathematik

Externe Organisation(en)

Universite d'Aix-Marseille
ETH Zürich

Typ

Artikel

Journal

Communications on Pure and Applied Analysis

Band

11

Seiten

1407-1419

Anzahl der Seiten

13

ISSN

1534-0392

Publikationsdatum

07.2012

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Analysis, Angewandte Mathematik

Elektronische Version(en)

https://doi.org/10.3934/cpaa.2012.11.1407 (Zugang: Offen)