We prove the phenomenon of dissipation enhancement for stochastic heat equations on the torus and perturbed by multiplicative noise of transport type. Our approach works also for the scaling limit of stochastic 2D (inviscid) fluid dynamical equations with transport noise to deterministic viscous equations. Quantitative estimates on the convergence rates are provided by combining analytic and probabilistic arguments, especially heat kernel properties and maximal estimates for stochastic convolutions. This talk is based on joint works with Professor Franco Flandoli and Lucio Galeati.

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