Anomalous diffusion by fractal homogenization
A Lean 4 / Mathlib formalization of S. Armstrong and V. Vicol, "Anomalous diffusion by fractal homogenization" (arXiv:2305.05048). For every alpha in (0, 1/3) it constructs one divergence-free, Z^2-periodic drift b in C^0_t C^{0,alpha}_x intersect C^{0,alpha}_t C^0_x on [0,1] x T^2, and proves three properties of the advection-diffusion equation with this drift: anomalous dissipation of scalar variance for every mean-zero H^1 datum (Theorem 1.1 of the paper); a uniform C^{0,mu}([0,1]; L^2) bound by C times the H^1 norm of the datum along a set of diffusivities accumulating at zero (Remark…
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