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We investigate the mixing properties of solutions to the stochastic transport equation d u= d W u, where the driving noise W (t, x) is white in time, colored and divergence-free in space. Furthermore, we prove the dissipation enhancement in the presence of a small viscous term. Applying our results, we also derive the mixing properties for a regularized stochastic 2D Euler equation.
Luo et al. (Mon,) studied this question.