For divergence-free flows, classical mixing criteria fail to persist under arbitrarily small velocity perturbations, and mixing any single bounded scalar forces mixing of an open dense set of scalars, under a weak non-precompactness notion of mixing.
A uniqueness result for the conti- nuity equation in two dimensions
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Mixing for generic passive scalars by incompressible flows
For divergence-free flows, classical mixing criteria fail to persist under arbitrarily small velocity perturbations, and mixing any single bounded scalar forces mixing of an open dense set of scalars, under a weak non-precompactness notion of mixing.