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

2021/02/15 by Víctor Navarro-Fernández, Navarro-Fernández, Víctor, André Schlichting +3
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2102.07759

openalex publication_date 2021/02/15 · openalex created_date 2022/12/24 · openalex updated_date 2026/07/28

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 L¹ functions entailing a new well-posedness result.

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