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Bounds on mixing norms for advection diffusion equations in the whole space via Fourier splitting and decay characters

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TURW03 - Modelling and analysis of turbulent transport, mixing and scaling

I will start this talk introducing a conjecture of Charles Doering and Christopher Miles (stated in “Diffusion-limited mixing by incompressible flows” , Nonlinearity 2018) on long-time convergence to the Batchelor scale of a suitable norm for mixing in passive scalars. Motivated by this conjecture, I will present mixing estimates on $R^n$ obtained in collaboration with Steffen Pottel by means of the Fourier-splitting method. These estimates were recently (substantially) improved by relaxing the assumptions on initial conditions.

This talk is part of the Isaac Newton Institute Seminar Series series.

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