Forward untangling and applications to the uniqueness problem for the continuity equation

DOI10.3934/dcds.2020384zbMath1465.35111OpenAlexW3098427815MaRDI QIDQ2030841

Paolo Bonicatto, Stefano Bianchini

Publication date: 8 June 2021

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2020384

zbMATH Keywords

superposition principleforward untangled Lagrangian representation

Mathematics Subject Classification ID

Weak solutions to PDEs (35D30) Initial value problems for linear first-order PDEs (35F10) Integration and disintegration of measures (28A50) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Initial value problems for first-order hyperbolic equations (35L03) Transport equations (35Q49)

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Cites Work

• Transport equation and Cauchy problem for BV vector fields
• Failure of the chain rule in the non steady two-dimensional setting
• A uniqueness result for the decomposition of vector fields in \(\mathbb{R}^d\)
• A uniqueness result for the continuity equation in two dimensions
• LAGRANGIAN FLOWS FOR VECTOR FIELDS WITH GRADIENT GIVEN BY A SINGULAR INTEGRAL
• An Estimate on the Flow Generated by Monotone Operators
• Duality theorems for marginal problems
• Eulerian and Lagrangian Solutions to the Continuity and Euler Equations with $L^1$ Vorticity
• Structure of level sets and Sard-type properties of Lipschitz maps
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