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

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

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 La...

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Veröffentlicht in:arXiv.org 2023-01
Hauptverfasser: Inversi, Marco, Stefani, Giorgio
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Continuity equation
Fields (mathematics)
Mathematical analysis
Stability
Uniqueness
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description 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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subjects Continuity equation
Fields (mathematics)
Mathematical analysis
Stability
Uniqueness
title Lagrangian stability for a system of non-local continuity equations under Osgood condition
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