An elementary approach to mixing and dissipation enhancement by transport noise

Dejun Luo; Bin Tang; Guohuan Zhao

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arXiv · 2402.07484

An elementary approach to mixing and dissipation enhancement by transport noise

Dejun Luo·Bin Tang·Guohuan Zhao

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Abstract

We investigate the mixing properties of solutions to the stochastic transport equation $d u= \circ d W \cdot\nabla u$, 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.

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Dejun Luo, Bin Tang, Guohuan Zhao. 2024-02-12. An elementary approach to mixing and dissipation enhancement by transport noise. https://arxiv.org/abs/2402.07484

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