A necessary and sufficient condition for enhanced dissipation under transport noise is the absence of non-trivial finite-dimensional invariant subspaces, with sharp rates for stochastic shear flows.
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A Stochastic RAGE Theorem and Enhanced Dissipation for Transport Noise
A necessary and sufficient condition for enhanced dissipation under transport noise is the absence of non-trivial finite-dimensional invariant subspaces, with sharp rates for stochastic shear flows.