Lagrangian stability for a system of non-local continuity equations under Osgood condition

2023/01/27 by Marco Inversi, Giorgio Stefani, Inversi, Marco +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Partial Differential Equations #Primary 35L65 #Secondary 34A30 #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2301.11822

openalex publication_date 2023/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

We extend known existence and uniqueness results of weak measure solutions for systems of non-local continuity equations beyond the usual Lipschitz regularity. Existence of weak measure solutions holds for uniformly continuous vector fields and convolution kernels, while uniqueness follows from a Lagrangian stability estimate under an additional Osgood condition.

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