Forward untangling and applications to the uniqueness problem for the continuity equation
Contents: Introduction: Synopsis of the paper Acknowledgements. 1. Notation. 2. Preliminaries on Lagrangian representations, proper sets and Optimal Transport. 2.1. Lagrangian representations. 2.2. Proper sets. 2.3. Optimal transport and duality. 3. Optimal transport and duality. 4. The global theory of forward untangling. 4.1. Subadditivity of untangling functional. 5. Uniqueness by forward untangling. 5.1. Decomposition and disintegration. 5.2. Composition rule. 6. Monotone vector ﬁelds. References.
transport equation, continuity equation, uniqueness, Superposition Principle