Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4592814 | Journal of Functional Analysis | 2008 | 23 Pages |
Abstract
Brownian motions above the group G of volume preserving diffeomorphisms of the torus Td, d⩾2, are constructed. The asymptotic behaviour for large time of those processes shows the nonexistence of a probability measure invariant under the deterministic incompressible fluid dynamics. The energy induces on the group of volume preserving diffeomorphisms of T2 a Riemannian structure which has a positive renormalized Ricci tensor.
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