Restrictions on the geometry of the periodic vorticity equation

verfasst von

Joachim Escher, Marcus Wunsch

Abstract

We prove that several evolution equations arising as mathematical models for fluid motion cannot be realized as metric Euler equations on the Lie group DIFF ^∞( ¹) of all smooth and orientation-preserving diffeomorphisms on the circle. These include the quasi-geostrophic model equation, cf. [A. Córdoba, D. Córdoba and M. A. Fontelos, Formation of singularities for a transport equation with nonlocal velocity, Ann. of Math. 162 (2005) 13771389], the axisymmetric Euler flow in ^d (see [H. Okamoto and J. Zhu, Some similarity solutions of the NavierStokes equations and related topics, Taiwanese J. Math. 4 (2000) 65103]), and De Gregorio's vorticity model equation as introduced in [S. De Gregorio, On a one-dimensional model for the three-dimensional vorticity equation, J. Stat. Phys. 59 (1990) 12511263].

Organisationseinheit(en)

Institut für Angewandte Mathematik

Externe Organisation(en)

ETH Zürich

Typ

Artikel

Journal

Communications in Contemporary Mathematics

Band

14

ISSN

0219-1997

Publikationsdatum

06.2012

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Mathematik (insg.), Angewandte Mathematik

Elektronische Version(en)

https://doi.org/10.1142/S0219199712500162 (Zugang: Unbekannt)