Lower Bounds for Advection-Diffusion Equations: An Exploration with AI-Generated Proofs

Chenyang An, Xiaoqian Xu

We establish explicit lower bounds for advection-diffusion equations in three settings: a polynomial ${\dot{H}}^{-1}$ bound for inviscid shears with $u\in L_t^{\infty }{W}_y^{1,1}$, a uni…