We show that for a large class of measurable vector fields in the sense of N. Weaver (i.e. derivations over the algebra of Lipschitz functions), 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.

Flows of measures generated by vector fields

Emanuele Paolini
Co-primo
;
2018-01-01

Abstract

We show that for a large class of measurable vector fields in the sense of N. Weaver (i.e. derivations over the algebra of Lipschitz functions), 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.
2018
Paolini, Emanuele; Stepanov, Eugene
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/890192
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