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

Autor:	Navarro-Fernández, Víctor, Schlichting, André, Seis, Christian
Rok vydání:	2021
Předmět:	Mathematics - Analysis of PDEs
Druh dokumentu:	Working Paper
Popis:	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. Comment: 22 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2102.07759 Zobrazit plný text záznamu View this record from Arxiv