Anomalous diffusion for passive scalar equations by fractal homogenization

Abstract: In this talk I will describe the main ideas in a recent joint work with Vlad Vicol. We construct an explicit divergence-free vector field on the torus, which is Holder continuous with exponent almost 1/3 in space and time, such that the corresponding advection-diffusion equation admits anomalous diffusion, for all initial data, along a subsequence of diffusivities tending to zero. The construction builds into the vector field a countable sequence of "active scales" which have resonances with the scalar, resulting in a cascade of energy moving to smaller scales. The proof is a renormalization scheme, based on homogenization methods.

mathematical physics

Audience: researchers in the discipline

One world IAMP mathematical physics seminar

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