Flows of measures generated by vector fields
Published online by Cambridge University Press: 14 February 2018
Abstract
The scope of the paper is twofold. We show that for a large class of measurable vector fields in the sense of Weaver (i.e. derivations over the algebra of Lipschitz functions), called in the paper laminated, the notion of integral curves may be naturally defined and characterized (when appropriate) by an ordinary differential equation. We further show that for such vector fields the notion of a flow of the given positive Borel measure similar to the classical one generated by a smooth vector field (in a space with smooth structure) may be defined in a reasonable way, so that the measure ‘flows along’ the appropriately understood integral curves of the given vector field and the classical continuity equation is satisfied in the weak sense.
MSC classification
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 148 , Issue 4 , August 2018 , pp. 773 - 818
- Copyright
- Copyright © Royal Society of Edinburgh 2018
- 1
- Cited by