Submitted Paper

Inserted: 27 jan 2023
Last Updated: 27 jan 2023

Year: 2023

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.

Keywords: Osgood condition, Non-local continuity equation, Lagrangian stability

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• Inversi, Stefani - Lagrangian stability for a system of non-local continuity equations under Osgood condition