Construction of C^{β0} (β0<1/3) divergence-free vector fields and κ_q → 0 such that advection-diffusion scalars exhibit anomalous dissipation while remaining bounded in C^α0 with β0 + 2α0 < 1, confirming the Armstrong-Vicol conjecture.
The geometry of turbulent advection: sharp estimates for the dimensions of level sets.Nonlinearity, 7(3):1045, may 1994
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Scalar anomalous dissipation and optimal regularity via iterated homogenization
Construction of C^{β0} (β0<1/3) divergence-free vector fields and κ_q → 0 such that advection-diffusion scalars exhibit anomalous dissipation while remaining bounded in C^α0 with β0 + 2α0 < 1, confirming the Armstrong-Vicol conjecture.