Exponential mixing by random cellular flows

Víctor Navarro-Fernández; Christian Seis

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arXiv · 2502.17273

Exponential mixing by random cellular flows

Víctor Navarro-Fernández·Christian Seis

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Abstract

We study a passive scalar equation on the two-dimensional torus, where the advecting velocity field is given by a cellular flow with a randomly moving center. We prove that the passive scalar undergoes mixing at a deterministic exponential rate, independent of any underlying diffusivity. Furthermore, we show that the velocity field enhances dissipation and we establish sharp decay rates that, for large times, are deterministic and remain uniform in the diffusivity constant. Our approach is purely Eulerian and relies on a suitable modification of Villani's hypocoercivity method, which incorporates a larger set of H\"ormander commutators than Villani's original method.

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Víctor Navarro-Fernández, Christian Seis. 2025-02-24. Exponential mixing by random cellular flows. https://arxiv.org/abs/2502.17273

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