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- W2989665024 abstract "We study the Riemannian geometry of 3D axisymmetric ideal fluids. We prove that the $L^2$ exponential map on the group of volume-preserving diffeomorphisms of a $3$-manifold is Fredholm along axisymmetric flows with sufficiently small swirl. Along the way, we define the notions of axisymmetric and swirl-free diffeomorphisms of any manifold with suitable symmetries and show that such diffeomorphisms form a totally geodesic submanifold of infinite $L^2$ diameter inside the space of volume-preserving diffeomorphisms whose diameter is known to be finite. As examples we derive the axisymmetric Euler equations on $3$-manifolds equipped with each of Thurston's eight model geometries." @default.
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- W2989665024 date "2019-11-23" @default.
- W2989665024 modified "2023-09-26" @default.
- W2989665024 title "Axisymmetric diffeomorphisms and ideal fluids on Riemannian 3-manifolds." @default.
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