Portugaliae Mathematica


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Volume 75, Issue 2, 2018, pp. 121–157
DOI: 10.4171/PM/2013

Published online: 2018-12-12

On flows generated by vector fields with compact support

Olivier Kneuss[1] and Wladimir Neves[2]

(1) Universidade Federal do Rio de Janeiro, Brazil
(2) Universidade Federal do Rio de Janeiro, Brazil

We are concerned with the theory of the existence and uniqueness of flows generated by divergence free vector fields with compact support. Hence, assuming that the velocity vector fields are measurable, bounded, and the flows in the Euclidean space are measure preserving, we show two counterexamples of uniqueness/existence of such flows. First we consider the autonomous case in dimension 3 and then the non-autonomous one in dimension 2.

Keywords: Flows, existence, uniqueness, compact support

Kneuss Olivier, Neves Wladimir: On flows generated by vector fields with compact support. Port. Math. 75 (2018), 121-157. doi: 10.4171/PM/2013