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Inverse Energy Cascade and Non-uniqueness for the Advection-Diffusion Equation
We prove non-uniqueness for the advection-diffusion equation with a drift in a logarithmically near-critical class below $L_t^2L_x^\infty$. The first construction is a diffusion-assisted inverse cascade of scalar energy that diverges as $t \to 0$. The second uses compressed inverse mixing, with diff
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