# Optimal stability estimates and a new uniqueness result for advection-diffusion equations

@inproceedings{NavarroFernandez2021OptimalSE, title={Optimal stability estimates and a new uniqueness result for advection-diffusion equations}, author={V'ictor Navarro-Fern'andez and Andr{\'e} Schlichting and Christian Seis}, year={2021} }

This paper contains two main contributions. First, it provides 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, the stability estimates are extended to the advection-diffusion equations with velocity fields whose gradients are singular integrals of L functions entailing a new well…

## One Citation

Error estimates for a finite volume scheme for advection-diffusion equations with rough coefficients

- Mathematics
- 2022

We study the implicit upwind finite volume scheme for numerically approximating the advection-diffusion equation with a vector field in the low regularity DiPerna-Lions setting. That is, we are…

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We study the implicit upwind finite volume scheme for numerically approximating the advection-diffusion equation with a vector field in the low regularity DiPerna-Lions setting. That is, we are…

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