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.
Enhanced Dissipation via the Malliavin Calculus
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abstract
In this work we investigate the phenomenon of enhanced dissipation using techniques from the Malliavin Calculus. In particular, we construct a concise, elementary argument, that allows us to recover the well-known enhanced dissipation timescale for shear flows, first obtained by Bedrossian and Coti Zelati in 2017, as well as the precise hypoelliptic regularisation in x.
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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.