The paper with Víctor Navarro-Fernández and Christian Seis on Optimal stability estimates and a new uniqueness result for advection-diffusion equations got published at Pure and Applied Analysis.
We present two main contributions. First, we provide optimal stability estimates for advection-diffusion equations in a setting in which the velocity field is Sobolev regular in the spatial variable. This estimate is formulated with the help of Kantorovich–Rubinstein distances with logarithmic cost functions. Second, we extend the stability estimates to the advection-diffusion equations with velocity fields whose gradients are singular integrals of L1 functions entailing a new well-posedness result.