Restrictions on the geometry of the periodic vorticity equation

Details Restrictions on the geometry of the periodic vorticity equation Restrictions on the geometry of the periodic vorticity equation

2010-09-06

arxiv.org/abs/1009.1029v1

Mathematics

Analysis of PDEs

14 pages, 1 table

Scientific paper

We prove that several evolution equations arising as mathematical models for
fluid motion cannot be realized as metric Euler equations on the Lie group of
all smooth and orientation-preserving diffeomorphisms on the circle. These
include the quasi-geostrophic model equation, the axisymmetric Euler flow in
higher space dimensions, and De Gregorio's vorticity model equation.

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