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

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arxiv 2301.11822 v1 pith:N7SDGBIL submitted 2023-01-27 math.AP math.CA

Marco Inversi , Giorgio Stefani This is my paper · ORCID
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keywords conditioncontinuityequationsexistencelagrangianmeasurenon-localosgood
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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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  1. On the well-posedness of (nonlinear) rough continuity equations

    math.AP 2025-02 accept novelty 8.0 of 10

    Rough continuity and transport equations are well-posed for Osgood and DiPerna-Lions drifts, yielding a rough Yudovich theorem for 2D Euler and a continuous random dynamical system.

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