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arXiv · 2102.07759

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

Víctor Navarro-Fernández·André Schlichting·Christian Seis
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Abstract

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

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Víctor Navarro-Fernández, André Schlichting, Christian Seis. 2021-02-15. Optimal stability estimates and a new uniqueness result for advection-diffusion equations. https://arxiv.org/abs/2102.07759

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