Abstract

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 $L^1$ functions entailing a new well-posedness result.

Keywords

Mathematical Subject Classification

Milestones

Authors